Question 1170383
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You need two identities:


1. *[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos\alpha\ -\ \cos\beta\ =\ -2\sin\(\frac{\alpha\,-\,\beta}{2}\)\sin\(\frac{\alpha\,+\,\beta}{2}\)]


2. *[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sin\alpha\ +\ \sin\beta\ =\ 2\sin\(\frac{\alpha\,+\,\beta}{2}\)\cos\(\frac{\alpha\,-\,\beta}{2}\)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\cos(2x)\,-\,\cos(4x)}{\sin(2x)\,+\,\sin(4x)}\ =\ \frac{-2\sin\(\frac{2x\,-\,4x}{2}\)\sin\(\frac{2x\,+\,4x}{2}\)}{2\sin\(\frac{2x\,+\,4x}{2}\)\cos\(\frac{2x\,-\,4x}{2}\)}]


You should be able to handle the rest of the simplification on your own.  Hint: *[tex \Large \tan(-x)\ =\ -\tan(x)]

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

From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> 
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