Question about Euler's formula I have a question about Euler's formula
$$e^{ix} = \cos(x)+i\sin(x)$$
I want to show 
$$\sin(ax)\sin(bx) = \frac{1}{2}(\cos((a-b)x)-\cos((a+b)x))$$
and
$$  \cos(ax)\cos(bx) = \frac{1}{2}(\cos((a-b)x)+\cos((a+b)x))$$
I'm not really sure how to get started here.
Can someone help me?

Try using the identity
$$\sin A \cos B  \equiv \tfrac{1}{2}\left(\sin(A + B) + \sin(A - B)\right)$$
