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<b>let </b><font color="Maroon" title="c1">x</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">x</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  <a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="sin_cos4.html#K2" title="SIN_COS4:func.2">cot</a> <font color="Maroon" title="c1">x</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:2"/>
 <a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">x</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="sin_cos4.html#K2" title="SIN_COS4:func.2">cot</a> <font color="Maroon" title="c1">x</font></span>)</span></span><br/>

<b>then </b> <a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">x</font></span>)</span></span>)</span> <a href="sin_cos.html#K2" title="SIN_COS:func.2">*</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">x</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T89" title="XCMPLX_1:th.89">XCMPLX_1:89</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="sin_cos4.html#K2" title="SIN_COS4:func.2">cot</a> <font color="Maroon" title="c1">x</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T76" title="XCMPLX_1:th.76">XCMPLX_1:76</a></i>
;<br/>
<b>hence </b><a NAME="E3:2"/>
 <a href="sin_cos.html#K24" title="SIN_COS:func.24">cos</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K21" title="SIN_COS:func.21">sin</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="sin_cos4.html#K2" title="SIN_COS4:func.2">cot</a> <font color="Maroon" title="c1">x</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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