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<div><span class="kw">theorem </span><a NAME="T57"><span class="comment"><font color="firebrick">:: SIN_COS9:57</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">r</font> &amp; <font color="Olive" title="b1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 &amp;  <a href="sin_cos9.html#K3" title="SIN_COS9:func.3">arctan</a> <font color="Olive" title="b1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K28" title="SIN_COS:func.28">PI</a> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 4</span>)</span> holds <br/><font color="Olive" title="b1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 <span class="kw">by</span> <span class="lab"><a class="ref" href="sin_cos9.html#T17" target="_self" onmouseover="rs('sin_cos9/T17')" onmouseout="rh()">Th17</a>, <a class="ref" href="sin_cos9.html#T51" target="_self" onmouseover="rs('sin_cos9/T51')" onmouseout="rh()">Th51</a></span>;<br/></div></div>
