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?

If you want to just use Euler's equation and no trig identities (except the fact that $\sin(x),\cos(x)$ are odd/even respectively), write $\sin(x)=\frac{\exp(ix)-\exp(-ix)}{2i}$ and $\cos(x)=\frac{\exp(ix)+\exp(-ix)}{2}$ and go to town simplifying the product $\sin(ax)\sin(bx)$. 
