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<b>let </b><font color="Maroon" title="c1">r</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">r</font> &amp; <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 implies  <a href="sin_cos9.html#K7" title="SIN_COS9:func.7">tan</a> <span class="p1">(<span class="default"><a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">r</font> )</span><br/>

<b>set </b><font color="Maroon" title="c2">x</font> =  <a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</font>;<br/>
<b>assume </b><a NAME="E1:72"/><i><font color="Green" title="E59">A1</font></i>: 
(  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">r</font> &amp; <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="sin_cos9.html#K7" title="SIN_COS9:func.7">tan</a> <span class="p1">(<span class="default"><a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">r</font></span><br/>

<i><font color="Green" title="E60">A4</font></i>: <span class="p1">(<span class="default"><a href="sin_cos.html#K25" title="SIN_COS:func.25">cos</a> <span class="p2">(<span class="default"><a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">sin</a> <span class="p2">(<span class="default"><a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span> = 
 <a href="sin_cos9.html#K8" title="SIN_COS9:func.8">cot</a> <span class="p1">(<span class="default"><a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</font></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos4.html#D2" title="SIN_COS4:def.2">SIN_COS4:def 2</a></i>
<br/>.= 
<font color="Maroon" title="c1">r</font>
<b>by </b><i><a class="txt" href="#E1:72"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="sin_cos9.html#T52" target="_self" title="SIN_COS9:th.52">Th50</a></i>
;<br/>
 <a href="sin_cos9.html#K7" title="SIN_COS9:func.7">tan</a> <span class="p1">(<span class="default"><a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">sin</a> <span class="p2">(<span class="default"><a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K25" title="SIN_COS:func.25">cos</a> <span class="p2">(<span class="default"><a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos4.html#D1" title="SIN_COS4:def.1">SIN_COS4:def 1</a></i>
<br/>.= 
1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">r</font>
<b>by </b><i><a class="txt" href="#E2:72"><i><font color="Green" title="E60">A4</font></i></a>, <a class="ref" href="xcmplx_1.html#T57" title="XCMPLX_1:th.57">XCMPLX_1:57</a></i>
;<br/>
<b>hence </b><a NAME="E4:72"/>
 <a href="sin_cos9.html#K7" title="SIN_COS9:func.7">tan</a> <span class="p1">(<span class="default"><a href="sin_cos9.html#K6" title="SIN_COS9:func.6">arccot</a> <font color="Maroon" title="c1">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">r</font>
 ; <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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