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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> = <a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> = <a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> = <a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = <a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<i><font color="Green">E59</font></i>: <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K8">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos3.html#T11" target="_self">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos3.html#T13" target="_self">Th13</a></i>
<br/>.= 
2 <a href="xcmplx_0.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"><span class="p5">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K8">+</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_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>

<br/>.= 
2 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</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_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos3.html#T8" target="_self">Th8</a></i>
<br/>.= 
2 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos3.html#T8" target="_self">Th8</a></i>
<br/>.= 
2 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos3.html#T59" target="_self">Th59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p1">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos3.html#T59" target="_self">Th59</a></i>
;<br/>
<a NAME="E2:75"/>
<span class="p1">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <span class="p1">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K8">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_2"><b>proof </b></a><div class="add">

<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K8">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K8">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos3.html#T12" target="_self">Th12</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos3.html#T14" target="_self">Th14</a></i>
<br/>.= 
2 <a href="xcmplx_0.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_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K11">-</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_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>

<br/>.= 
2 <a href="xcmplx_0.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_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p5">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos3.html#T8" target="_self">Th8</a></i>
<br/>.= 
2 <a href="xcmplx_0.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_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos3.html#T8" target="_self">Th8</a></i>
<br/>.= 
2 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos3.html#T59" target="_self">Th59</a></i>
;<br/>
<b>hence </b><a NAME="E2:75_2"/>
<span class="p1">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <span class="p1">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K8">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="sin_cos3.html#T59" target="_self">Th59</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:75"/>
( <span class="p1">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p1">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K8">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <span class="p1">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="sin_cos3.html#K3" target="_self">sinh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K11">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="sin_cos3.html#K4" target="_self">cosh_C</a>  <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K8">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="sin_cos3.html#E1:75"><i><font color="Green">E59</font></i></a></i>;<br/>


</div>
