Question

Find the general solution:
$\sin 2x+\cos x=0$

Answer 1

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

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

$\Rightarrow \cos x=0$ or $\sin x=\frac{-1}{2}$

$\Rightarrow x=\frac{(2n+1)\pi }{2}$ or $x=n\pi -(-1{)}^n\frac{\pi }{6}$