Show that $\sin(\frac{x}{2})(\sin(x)+\sin(2x)+...+\sin(nx))=\sin(\frac{nx}{2})\sin(\frac{n+1}{2}x)$
Prove by induction $ \sin x + \sin 2x + ... + \sin nx = \frac {\sin (\frac {n + 1} {2} x)} {\sin \frac{x}{2}} \sin \frac{nx}{2} $