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How would I solve the following double angle identity. $$ \frac{\sin(A+B)}{\cos(A-B)}=\frac{\tan A+\tan B}{1+\tan A\tan B} $$ So far my work has been. $$ \frac{\sin A\cos B+\cos A\sin B}{\cos A\cos B+\sin A\sin B} $$ But what would I do to continue.

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Divide numerator and denominator by $\cos A \cos B$. –  Aang Jul 25 '12 at 17:26
Oh I see now dividing by cos I get the correct answer thanks to all who posted. –  El Bananero Jul 25 '12 at 17:31
One can prove and identity or solve an equation. But to speak of solving an identity could leave some doubt about what you mean. –  Michael Hardy Jul 25 '12 at 18:15
@Rick Decker: please do not change the variables from $A,B$ to $x,y$ as avatar's comment and my answer were in terms of $A,B$ –  Ross Millikan Jul 25 '12 at 18:20
@Ross. Sorry about that. avatar's comment, your answer, and my edit came virtually on top of each other; I didn't see the notifications while I was editing. Note to self: for questions that are likely to be answered immediately after they're posted, delay editing until the dust settles. –  Rick Decker Jul 25 '12 at 19:56
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2 Answers

Now divide by $\cos A \cos B$ and you are there

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What i get is, how to solve the problem?? Is that correct then here u are:

$$\dfrac{\dfrac{\sin x\cos y + \cos x\sin y}{\cos x\cos y}} {\dfrac{\cos x\cos y + \sin x\sin y}{\cos x\cos y}}$$

$$\dfrac{\dfrac{\sin x\cos y}{\cos x\cos y} +\dfrac{\cos x\sin y}{\cos x\cos y}} {\dfrac{\cos x\cos y} {\cos x\cos y}+ \dfrac{\sin x\sin y}{\cos x\cos y}}$$ $$\dfrac{\tan x+\tan y}{1+\tan x\tan y}$$

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