[Math] Proving the identity: $\sin3x + \sin x = 2\sin2x\cos x$

Question

I need some help proving this identity:

$$\sin3x + \sin x = 2\sin2x\cos x$$

I don't know where to start. I thought about expanding $\sin 3x$ into $\sin (2x + x)$ but I don't think that does me any good. Any hints would be appreciated.

Thanks!

Answer 1

Consider $\sin(2x + x)$ and $\sin(2x-x)$.