# Simplifying Trig Identity

I have an equation I have been given to solve, I know how to start but I do not know what to do after I use the Trig Identities. Any help?

Here is what I was given $$\frac{\cos(A + B) + \cos(A - B)}{\sin A \sin B}$$ I got to this step $$\frac{\cos A\cos B-\sin A\sin B + \cos A\cos B+\sin A\sin B}{\sin A\sin B}$$ What do I do next to simplify?

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$\sin a\sin b-\sin a\sin b=0$ –  NotNotLogical Apr 16 '14 at 18:22

## 1 Answer

\begin{align} \cos(A+B) + \cos(A-B) & = \cos(A) \cos(B) - \sin(A) \sin(B) + \cos(A) \cos(B) + \sin(A) \sin(B)\\ & = 2 \cos(A) \cos(B) \end{align} Hence, $$\dfrac{\cos(A+B) + \cos(A-B)}{\sin(A) \sin(B)} = 2 \cot(A) \cot(B)$$

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Thank you so much –  need help Apr 16 '14 at 18:25
I'll accept your answer in a few minutes when it allows me –  need help Apr 16 '14 at 18:26