Show that $\sum_{n=0}^\infty \frac{\sin {nx}}{a^n} = \frac{a \sin{x}}{1 + a^{2} - 2a \cos{x}}$
I've been trying to use the geometric series rule for $\sum_{n=0}^\infty x^{-n} = \frac{x}{x -1}$ as well as Euler for the $\sin(nx)$, but I just can't seem to get the series to reduce to the fraction on the right. Could you help?