Question

Which of the following is a solution to sin(2x) - cos x=0

Answer 1

$\sin2x-\cos x=0\ \ \ |\text{use:}\ \sin2x=2\sin x\cos x\\\\2\sin x\cos x-\cos x=0\\\\\cos x(2\sin x-1)=0\iff\cos x=0\ \vee\ 2\sin x-1=0\\\\(1)\ \cos x=0\to x=90^0\ \vee\ x=270^o\\\\(2)\ 2\sin x-1=0\ \ \ |+1\\2\sin x=1\ \ \ |:2\\\sin x=\frac{1}{2}\to x=30^o\ \vee\ x=150^o\\\\Answer:\ B.)\ 90^o.$