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<b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> ;<br/>



<a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="arytm_0.html#K5">*]</a></span> = 
<a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">x</font></span>)</span></span>)</span>,<font color="Maroon">y</font></span><a href="arytm_0.html#K5">*]</a></span>

<br/>.= 
<a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2"><a href="arytm_0.html#K5">[*</a><span class="default"><font color="Maroon">y</font>,<span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">x</font></span>)</span></span><a href="arytm_0.html#K5">*]</a></span> <a href="complex1.html#K9">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span>
<b>by </b><i><a class="ref" href="sin_cos3.html#T2" target="_self">Th2</a></i>
<br/>.= 
<a href="sin_cos3.html#K2" target="_self">cos_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><font color="Maroon">y</font>,<span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">x</font></span>)</span></span><a href="arytm_0.html#K5">*]</a></span>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E2:62"/>
<a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="arytm_0.html#K5">*]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K4">cosh</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K22">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos2.html#K1">sinh</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K19">sin</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">y</font></span>)</span></span>)</span></span><a href="arytm_0.html#K5">*]</a></span>
 <b>by </b><i><a class="ref" href="sin_cos3.html#T8" target="_self">Th8</a></i>;<br/>


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