# Find the general solution for each of the following equation $\sin 2x+\cos x=0$

$\begin{array}{1 1}(A)\;x=n\pi+(-1)^n\large\frac{7\pi}{6}&(B)\;x=2n\pi+(-1)^n\large\frac{\pi}{6}\\(C)\;x=3n\pi+(-1)^n\large\frac{\pi}{6}&(D)\;x=4n\pi+(-1)^n\large\frac{\pi}{6}\end{array}$

Toolbox:
• $\sin 2x=2\sin x\cos x$
$\sin 2x+\cos x=0$
$2\sin x\cos x+\cos x=0$
$\cos x(2\sin x+1)=0$
When $2\sin x+1=0,\sin x=-\large\frac{1}{2}$$=\sin (\pi+\large\frac{\pi}{6})$
$\Rightarrow \sin \large\frac{7\pi}{6}$
$x=n\pi+(-)^n\large\frac{7\pi}{6}$
Hence (A) is the correct answer.