Question

Prove sin (n+1)x - sin nx in terms of nx and sin nx

Answer 1

I need to prove that $\sin(n x) +\sin((n+2) x) = 2\cos(x)\sin((n+1) x)$. I have already checked that this is correct for $n=1$ and $n=2$, but I'm not able to prove this identity by induction. Now I was thinking of making a shift to the imaginary numbers by saying