Question

Number of solutions of $2\sin 2x+2\sqrt{2}\sin (x-\frac{\pi }{4})=1$ in $[0,\pi ]$ is

Answer 1

$4\sin x\cos x+2\sin x-2\cos x=1$
$2\sin x(2\cos x+1)-(2\cos x+1)=0$
$\sin x=\frac{1}{2}$ or $\cos x=\frac{-1}{2}$
$x=\frac{\pi }{6},\frac{5\pi }{6},\frac{2\pi }{3}$