Question 373748
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I don't know of a direct geometric proof of the tangent of a difference formula.  I've always seen it done by geometric proofs of *[tex \Large \sin(\alpha\ -\ \beta)] and *[tex \Large \cos(\alpha\ -\ \beta)] and then using *[tex \Large \tan\varphi\ =\ \frac{\sin\varphi}{\cos\varphi}]


Geometric proofs of the sine and cosine of differences can be found at:


<a href="http://www.maa.org/pubs/mm_supplements/smiley/trigproofs.html">Sine and Cosine of Difference Proofs</a>


Then the algebra to get it into the final form for tangent is found at:


<a href="http://oakroadsystems.com/twt/sumdiff.htm">Sum/Difference Formulas (Scroll Down to TANGENT AħB)</a>





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