Solve the equation $\sin mx+\sin nx=0$

Question

$\begin{array}{1 1}(A)\;\large\frac{2p\pi}{m+n},\frac{(2q+1)\pi}{m-n}&(B)\;\large\frac{6p\pi}{m+n},\frac{(3q+1)\pi}{2}\\(C)\;\large\frac{p\pi}{m+n},\frac{(7q+1)\pi}{4}&(D)\;\large\frac{8p\pi}{m+n},\frac{(2q+5)\pi}{2}\end{array}$