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<b>let </b><font color="Maroon">x</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<a NAME="E1:41"/><i><font color="Green">E25</font></i>: 
 <a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i/>;<br/>
<i><font color="Green">E26</font></i>:  <a href="sin_cos2.html#K3">sinh</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> = 
<span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="txt" href="sin_cos8.html#E3"><i><font color="Green">Lemma24</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sin_cos8.html#E2:41"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xcmplx_1.html#T89">XCMPLX_1:89</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T101">XCMPLX_1:101</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T121">XCMPLX_1:121</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sin_cos8.html#E2:41"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sin_cos8.html#E2:41"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i/>
;<br/>
<i><font color="Green">E30</font></i>:  <a href="sin_cos2.html#K3">sinh</a> <span class="p1">(<span class="default">3 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> = 
<span class="p1">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="prepower.html#K3">|^</a> <span class="p3">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos5.html#T43">SIN_COS5:43</a></i>
<br/>.= 
<span class="p1">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="prepower.html#K3">|^</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="prepower.html#K3">|^</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> 3</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="prepower.html#K3">|^</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T10">NEWTON:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span> <a href="real_1.html#K3">+</a> 3</span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span>

;<br/>
<i><font color="Green">E35</font></i>:  <a href="sin_cos2.html#K3">sinh</a> <span class="p1">(<span class="default">3 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos8.html#T1" target="_self">Th1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <span class="p0">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default">3 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span>

;<br/>
<i><font color="Green">E36</font></i>:  <a href="sin_cos2.html#K6">cosh</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> = 
<span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
<b>by </b><i><a class="txt" href="sin_cos8.html#E3"><i><font color="Green">Lemma24</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
<b>by </b><i/>
<br/>.= 
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>

;<br/>
<i><font color="Green">E41</font></i>:  <a href="sin_cos2.html#K6">cosh</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> = 
<span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
<b>by </b><i><a class="txt" href="sin_cos8.html#E3"><i><font color="Green">Lemma24</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>

;<br/>
<a NAME="E7:41"/>
 <a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i/>;<br/>
<a NAME="E8:41"/><b>then </b>
<span class="p1">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/>
<a NAME="E9:41"/><b>then </b><i><font color="Green">E42</font></i>: 
<span class="p1">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
;<br/>
<i><font color="Green">E43</font></i>:  <a href="sin_cos2.html#K6">cosh</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><a href="sin_cos5.html#K2">sech</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i>, <a class="txt" href="sin_cos8.html#E7"><i><font color="Green">Lemma31</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos5.html#K2">sech</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K4">*</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="square_1.html#T59">SQUARE_1:59</a>, <a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos5.html#K2">sech</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sin_cos8.html#E8"><i><font color="Green">Lemma32</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos5.html#K2">sech</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos5.html#K2">sech</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos5.html#K2">sech</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T101">XCMPLX_1:101</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos5.html#K2">sech</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos5.html#K2">sech</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos5.html#K2">sech</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos5.html#D2">SIN_COS5:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos5.html#K2">sech</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos5.html#T38">SIN_COS5:38</a></i>
;<br/>
<i><font color="Green">E55</font></i>:  <a href="sin_cos2.html#K6">cosh</a> <span class="p1">(<span class="default">3 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> = 
<span class="p1">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="prepower.html#K3">|^</a> <span class="p3">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos5.html#T44">SIN_COS5:44</a></i>
<br/>.= 
<span class="p1">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="prepower.html#K3">|^</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="prepower.html#K3">|^</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 3</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="prepower.html#K3">|^</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 3</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 3</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T10">NEWTON:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 3</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> 1</span>)</span>

;<br/>
 <a href="sin_cos2.html#K9">tanh</a> <span class="p1">(<span class="default">3 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> = 
 <a href="sin_cos2.html#K9">tanh</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">x</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">x</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="prepower.html#K3">|^</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T10">NEWTON:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="prepower.html#K3">|^</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="prepower.html#K3">|^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="prepower.html#K3">|^</a> 3</span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">3 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span>

;<br/>
<b>hence </b><a NAME="E13:41"/>
(  <a href="sin_cos2.html#K3">sinh</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> &amp;  <a href="sin_cos2.html#K3">sinh</a> <span class="p1">(<span class="default">3 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> &amp;  <a href="sin_cos2.html#K3">sinh</a> <span class="p1">(<span class="default">3 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span> &amp;  <a href="sin_cos2.html#K6">cosh</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> &amp;  <a href="sin_cos2.html#K6">cosh</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> &amp;  <a href="sin_cos2.html#K6">cosh</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> &amp;  <a href="sin_cos2.html#K6">cosh</a> <span class="p1">(<span class="default">3 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="sin_cos2.html#K6">cosh</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K3">sinh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> 1</span>)</span> &amp;  <a href="sin_cos2.html#K9">tanh</a> <span class="p1">(<span class="default">3 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="prepower.html#K3">|^</a> 3</span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">3 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos2.html#K9">tanh</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="sin_cos8.html#E4"><i><font color="Green">Lemma27</font></i></a>, <a class="ref" href="sin_cos8.html#T1" target="_self">Th1</a>, <a class="txt" href="sin_cos8.html#E6"><i><font color="Green">Lemma29</font></i></a>, <a class="txt" href="sin_cos8.html#E3:41"><i><font color="Green">E30</font></i></a>, <a class="txt" href="sin_cos8.html#E7"><i><font color="Green">Lemma31</font></i></a>, <a class="txt" href="sin_cos8.html#E9"><i><font color="Green">Lemma33</font></i></a>, <a class="txt" href="sin_cos8.html#E10"><i><font color="Green">Lemma34</font></i></a></i>;<br/>


</div>
