Question

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

Answer 1

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

$⟹2\sin x\cos x+\cos x=0$

$⟹(2\sin x+1)\cos x=0$

$⟹(2\sin x+1)=0$ or $\cos x=0$

$⟹\sin x=-\frac{1}{2}$ or $\cos x=0$

$⟹x=\frac{7\pi }{6}+2n\pi ,x=\frac{11\pi }{6}+2n\pi$ or $x=\pm \frac{\pi }{2}+2n\pi$ (Since, $\sin$ is negative in third and fourth quadrant)