<PRE><B>Question 681619</B>
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1\ -\ \tan^2\varphi}{1\ +\ \tan^2\varphi}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1\ -\ \frac{\sin^2\varphi}{\cos^2\varphi}}{1\ +\ \frac{\sin^2\varphi}{\cos^2\varphi}}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\frac{\cos^2\varphi\ -\ \sin^2\varphi}{\cos^2\varphi}}{\frac{\cos^2\varphi\ +\ \sin^2\varphi}{\cos^2\varphi}}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\cos^2\varphi\ -\ \sin^2\varphi}{\cos^2\varphi\ +\ \sin^2\varphi}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\cos(2\varphi)}{\cos^2\varphi\ +\ \sin^2\varphi}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\cos(2\varphi)}{1}\ =\ \cos(2\varphi)]


By the way, if you want to know about the &quot;double &lt;b&gt;&lt;i&gt;angel&lt;/i&gt;&lt;/b&gt;&quot; formula, consult your local priest, minister, pastor, imam, rabbi, tribal shaman, or whatever passes for a cleric in your personal tradition.  Trigonometry is concerned with &lt;b&gt;&lt;i&gt;angles&lt;/i&gt;&lt;/b&gt;.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
&lt;font face=&quot;Math1&quot; size=&quot;+2&quot;&gt;Egw to Beta kai to Sigma&lt;/font&gt;
My calculator said it, I believe it, that settles it
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