Answer
Using a Double-Angle Formula we see that the equation $\sin x+\sin 2x=0$ is equivalent to the equation $\sin x+2\sin x\cos x=0$. Factoring, we see that solving the equation is equivalent to solving the two basic equations $\sin x=0$ and $1+2\cos x=0$.
Work Step by Step
Because of the identity $\sin 2x=2\sin x\cos x$, we can rewrite $\sin x+\sin 2x=0$ as $\sin x+2\sin x\cos x=0$, and then factor it into $\sin x(1+2\cos x)=0$. This breaks into $\sin x=0$ and $1+2\cos x=0$.
