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<span class="kw">let </span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <span class="p1">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">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"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">th1</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos4.html#K1" title="SIN_COS4:func.1">tan</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="sin_cos4.html#K1" title="SIN_COS4:func.1">tan</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_cos4.html#K1" title="SIN_COS4:func.1">tan</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><a href="sin_cos4.html#K1" title="SIN_COS4:func.1">tan</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:51"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
 <a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">and </span><br/><a NAME="E2:51"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
 <a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">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"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">th1</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos4.html#K1" title="SIN_COS4:func.1">tan</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="sin_cos4.html#K1" title="SIN_COS4:func.1">tan</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_cos4.html#K1" title="SIN_COS4:func.1">tan</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><a href="sin_cos4.html#K1" title="SIN_COS4:func.1">tan</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span></span><br/>

<span class="p1">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">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"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">th1</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">th2</font></span>)</span></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#K21" title="SIN_COS:func.21">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="p3">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</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#K24" title="SIN_COS:func.24">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#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c2">th2</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"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">th1</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="sin_cos.html#T80" title="SIN_COS:th.80">SIN_COS:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">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="p3">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</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#K24" title="SIN_COS:func.24">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#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c2">th2</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"><span class="p3">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">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="p3">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="sin_cos.html#T88" title="SIN_COS:th.88">SIN_COS:88</a></span>
<br/>.= 
<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_cos.html#K21" title="SIN_COS:func.21">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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</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="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p4">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p4">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:51"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E2:51"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="xcmplx_1.html#T6" title="XCMPLX_1:th.6">XCMPLX_1:6</a>, <a class="ref" href="xcmplx_1.html#T55" title="XCMPLX_1:th.55">XCMPLX_1:55</a></span>
<br/>.= 
<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_cos.html#K21" title="SIN_COS:func.21">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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</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="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></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"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p4">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</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="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</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="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p5">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T63" title="XCMPLX_1:th.63">XCMPLX_1:63</a></span>
<br/>.= 
<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_cos.html#K21" title="SIN_COS:func.21">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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</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="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></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"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p4">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</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="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</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="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></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="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p5">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T63" title="XCMPLX_1:th.63">XCMPLX_1:63</a></span>
<br/>.= 
<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_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></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"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p4">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</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="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</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="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></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="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p5">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T77" title="XCMPLX_1:th.77">XCMPLX_1:77</a></span>
<br/>.= 
<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_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></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"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c2">th2</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</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="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></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="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p5">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T77" title="XCMPLX_1:th.77">XCMPLX_1:77</a></span>
<br/>.= 
<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_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></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"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c2">th2</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></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"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p5">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T77" title="XCMPLX_1:th.77">XCMPLX_1:77</a></span>
<br/>.= 
<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_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></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"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c2">th2</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></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"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p5">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T77" title="XCMPLX_1:th.77">XCMPLX_1:77</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</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"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c2">th2</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></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"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p5">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:51"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="xcmplx_1.html#T89" title="XCMPLX_1:th.89">XCMPLX_1:89</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</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#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c2">th2</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></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"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p5">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:51"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="xcmplx_1.html#T89" title="XCMPLX_1:th.89">XCMPLX_1:89</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</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#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c2">th2</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</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"><span class="p3">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</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"><span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p5">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</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="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:51"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="xcmplx_1.html#T89" title="XCMPLX_1:th.89">XCMPLX_1:89</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</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#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c2">th2</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</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"><span class="p3">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">th1</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="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</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="p3">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:51"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="xcmplx_1.html#T89" title="XCMPLX_1:th.89">XCMPLX_1:89</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos4.html#K1" title="SIN_COS4:func.1">tan</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="sin_cos4.html#K1" title="SIN_COS4:func.1">tan</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_cos4.html#K1" title="SIN_COS4:func.1">tan</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c2">th2</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T188" title="XCMPLX_1:th.188">XCMPLX_1:188</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos4.html#K1" title="SIN_COS4:func.1">tan</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="sin_cos4.html#K1" title="SIN_COS4:func.1">tan</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_cos4.html#K1" title="SIN_COS4:func.1">tan</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><a href="sin_cos4.html#K1" title="SIN_COS4:func.1">tan</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span>

;<br/>
<span class="kw">hence </span><a NAME="E4:51"/>
<span class="p1">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">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"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">th1</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos4.html#K1" title="SIN_COS4:func.1">tan</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="sin_cos4.html#K1" title="SIN_COS4:func.1">tan</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_cos4.html#K1" title="SIN_COS4:func.1">tan</a> <font color="Maroon" title="c1">th1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><a href="sin_cos4.html#K1" title="SIN_COS4:func.1">tan</a> <font color="Maroon" title="c2">th2</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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