Find the solution of $\sin 2x+\cos x=0$.

given, $\sin 2x+\cos x=0$

$2\sin x\cos x+\cos x=0$

$(2\sin x+1)\cos x=0$

$2\sin x+1=0$

$\sin x=\frac{-1}{2}$ in case $x=\frac{7\pi }{6}$

$\cos x=0,x=\frac{\pi }{2}$

$\therefore x=\frac{\pi }{2},\frac{7\pi }{6}$