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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>



<a NAME="E1:56"/>
( <span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c1">x</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default">0 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a> </span>)</span> &amp; <span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default">0,<font color="Maroon" title="c2">y</font></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="complex1.html#T27" title="COMPLEX1:th.27">COMPLEX1:27</a></i>;<br/>
<b>then </b><a href="sin_cos3.html#K1" title="SIN_COS3:func.1">sin_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span> = 
<a href="sin_cos3.html#K1" title="SIN_COS3:func.1">sin_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p1">(<span class="default"><span class="p2"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c1">x</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p2"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default">0,<font color="Maroon" title="c2">y</font></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T27" title="COMPLEX1:th.27">COMPLEX1:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos3.html#K1" title="SIN_COS3:func.1">sin_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c1">x</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K2" title="SIN_COS3:func.2">cos_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default">0,<font color="Maroon" title="c2">y</font></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos3.html#K2" title="SIN_COS3:func.2">cos_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c1">x</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K1" title="SIN_COS3:func.1">sin_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default">0,<font color="Maroon" title="c2">y</font></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos3.html#T4" target="_self" title="SIN_COS3:th.4">Th4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos3.html#K1" title="SIN_COS3:func.1">sin_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c1">x</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K2" title="SIN_COS3:func.2">cos_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p4"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c2">y</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos3.html#K2" title="SIN_COS3:func.2">cos_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c1">x</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K1" title="SIN_COS3:func.1">sin_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default">0,<font color="Maroon" title="c2">y</font></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sin_cos3.html#E39"><i><font color="Green" title="E32">Lm9</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos3.html#K1" title="SIN_COS3:func.1">sin_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c1">x</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K2" title="SIN_COS3:func.2">cos_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p4"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c2">y</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos3.html#K2" title="SIN_COS3:func.2">cos_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c1">x</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K1" title="SIN_COS3:func.1">sin_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p4"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c2">y</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sin_cos3.html#E39"><i><font color="Green" title="E32">Lm9</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos3.html#K1" title="SIN_COS3:func.1">sin_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c1">x</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K4" title="SIN_COS3:func.4">cosh_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c2">y</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos3.html#K2" title="SIN_COS3:func.2">cos_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c1">x</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K1" title="SIN_COS3:func.1">sin_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p4"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c2">y</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos3.html#T16" target="_self" title="SIN_COS3:th.16">Th16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos3.html#K1" title="SIN_COS3:func.1">sin_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c1">x</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K4" title="SIN_COS3:func.4">cosh_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c2">y</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos3.html#K2" title="SIN_COS3:func.2">cos_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c1">x</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><a href="sin_cos3.html#K3" title="SIN_COS3:func.3">sinh_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p4"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c2">y</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos3.html#T15" target="_self" title="SIN_COS3:th.15">Th15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K19" title="SIN_COS:func.19">sin</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K4" title="SIN_COS3:func.4">cosh_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c2">y</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos3.html#K2" title="SIN_COS3:func.2">cos_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c1">x</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><a href="sin_cos3.html#K3" title="SIN_COS3:func.3">sinh_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p4"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c2">y</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos3.html#T38" target="_self" title="SIN_COS3:th.38">Th38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K19" title="SIN_COS:func.19">sin</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K4" title="SIN_COS3:func.4">cosh_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c2">y</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">cos</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><a href="sin_cos3.html#K3" title="SIN_COS3:func.3">sinh_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p4"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c2">y</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos3.html#T39" target="_self" title="SIN_COS3:th.39">Th39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K19" title="SIN_COS:func.19">sin</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K4" title="SIN_COS3:func.4">cosh_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p3"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c2">y</font>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">cos</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K1" title="SIN_COS2:func.1">sinh</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos3.html#T40" target="_self" title="SIN_COS3:th.40">Th40</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K19" title="SIN_COS:func.19">sin</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K4" title="SIN_COS2:func.4">cosh</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default">0 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default">0 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">cos</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K1" title="SIN_COS2:func.1">sinh</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos3.html#T41" target="_self" title="SIN_COS3:th.41">Th41</a></i>
<br/>.= 
<span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K19" title="SIN_COS:func.19">sin</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K4" title="SIN_COS2:func.4">cosh</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 0</span>)</span>,<span class="p2">(<span class="default">0 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">cos</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p4">(<span class="default"><a href="sin_cos2.html#K1" title="SIN_COS2:func.1">sinh</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span></span>)</span></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
<b>by </b><i><a class="ref" href="complex1.html#T27" title="COMPLEX1:th.27">COMPLEX1:27</a></i>
;<br/>
<b>hence </b><a NAME="E3:56"/>
<a href="sin_cos3.html#K1" title="SIN_COS3:func.1">sin_C</a>  <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K19" title="SIN_COS:func.19">sin</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K4" title="SIN_COS2:func.4">cosh</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">cos</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><a href="sin_cos2.html#K1" title="SIN_COS2:func.1">sinh</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
 ;<br/>


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