Question 604440
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1\ +\ \tan\varphi}{1\ +\ \cot\varphi}\ \equiv^?\ \tan\varphi] 


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1\ +\ \frac{\sin\varphi}{\cos\varphi}}{1\ +\ \frac{\cos\varphi}{\sin\varphi}}\ \equiv^?\ \tan\varphi]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\frac{\cos\varphi\ +\ \sin\varphi}{\cos\varphi}}{\frac{\sin\varphi\ +\ \cos\varphi}{\sin\varphi}}\ \equiv^?\ \tan\varphi]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\sin\varphi}{\cos\varphi}\ \equiv\ \tan\varphi]



John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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