<?xml version="1.0"?>
<div class="add">

<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 href="sin_cos3.html#K4" title="SIN_COS3:func.4">cosh_C</a>  <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</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#K4" title="SIN_COS3:func.4">cosh_C</a>  <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</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"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">x</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">y</font></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>

<br/>.= 
<a href="sin_cos3.html#K4" title="SIN_COS3:func.4">cosh_C</a>  <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</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="c2">y</font>,<span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">x</font></span>)</span></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a> </span>)</span>
<b>by </b><i><a class="txt" href="sin_cos3.html#E52"><i><font color="Green" title="E38">Lm11</font></i></a></i>
<br/>.= 
<a href="sin_cos3.html#K2" title="SIN_COS3:func.2">cos_C</a>  <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c2">y</font>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">x</font></span>)</span></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
<b>by </b><i><a class="ref" href="sin_cos3.html#T18" target="_self" title="SIN_COS3:th.18">Th18</a></i>
;<br/>
<b>hence </b><a NAME="E2:62"/>
<a href="sin_cos3.html#K4" title="SIN_COS3:func.4">cosh_C</a>  <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</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_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="c1">x</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <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="c2">y</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><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="c1">x</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <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="c2">y</font></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="sin_cos3.html#T46" target="_self" title="SIN_COS3:th.46">Th46</a></i>;<br/>


</div>
