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<b>let </b><font color="Maroon">a</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:71"/><i><font color="Green">E28</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K35">PI</a>  )
 <b>and </b><br/><a NAME="E2:71"/><i><font color="Green">E30</font></i>: 
 <a href="sin_cos.html#K23">cos</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 1
 ;<br/>

<a NAME="E3:71"/>
<span class="p1">(<span class="default">1 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K20">sin</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K20">sin</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="txt" href="comptrig.html#E27"><i><font color="Green">Lemma56</font></i></a>, <a class="ref" href="sin_cos.html#T32">SIN_COS:32</a></i>;<br/>
<a NAME="E4:71"/><b>then </b>
 <a href="sin_cos.html#K20">sin</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/>
<b>hence </b><a NAME="E5:71"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="comptrig.html#E27"><i><font color="Green">Lemma56</font></i></a>, <a class="ref" href="sin_cos.html#T82">SIN_COS:82</a>, <a class="txt" href="comptrig.html#E26"><i><font color="Green">Lemma55</font></i></a>, </i>;<br/>


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