Solve for $x$ when $\sin 2x = \cos x$ where $ x$ is in the domain $ [0, 2\pi]$ Quick question on trig (which I haven't dealt with in a long time): 
since $\sin 2x = 2\sin x\cos x $
$2\sin x\cos x = \cos x$
$2\sin x\cos x/\cos x = 1$
$\sin x = 1/2$
since $\sin x = 1/2$ in quadrants $1$ and $2$, $x = \pi/6$ and $x = 5\pi/6$
Is this correct? If not, hint please.

After getting $$2\sin x\cos x=\cos x,$$
you cannot divide the both sides by $\cos x$ because $\cos x$ can be zero.
So, we have
$$2\sin x\cos x-\cos x=0\iff \cos x(2\sin x-1)=0\iff \cos x=0\ \text{or}\ 2\sin x-1=0.$$
