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<b>let </b><font color="Maroon" title="c1">th1</font>, <font color="Maroon" title="c2">th2</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>



<b>assume </b><a NAME="E1:27"/>
(  <a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <font color="Maroon" title="c1">th1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0 &amp;  <a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <font color="Maroon" title="c2">th2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0 )
 ;<br/>

<b>then </b><span class="p1">(<span class="default"><a href="sin_cos4.html#K2" title="SIN_COS4:func.2">cot</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="sin_cos4.html#K2" title="SIN_COS4:func.2">cot</a> <font color="Maroon" title="c2">th2</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <font color="Maroon" title="c1">th1</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T117" title="XCMPLX_1:th.117">XCMPLX_1:117</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">th1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos.html#T80" title="SIN_COS:th.80">SIN_COS:80</a></i>
;<br/>
<b>hence </b><a NAME="E3:27"/>
<span class="p1">(<span class="default"><a href="sin_cos4.html#K2" title="SIN_COS4:func.2">cot</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="sin_cos4.html#K2" title="SIN_COS4:func.2">cot</a> <font color="Maroon" title="c2">th2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">th1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span>
 ;<br/>


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