Question

Solve the following equation:
$\sin x\cos x\sin 2x=\frac{1}{8}$

Answer 1

$2\sin x\cos x\sin 2x=1/4$

$(\sin 2x{)}^2=1/4$

$⟹\sin 2x=\pm 1/2$

$⟹2x=n\pi +(-1{)}^n\pi /6$

$⟹x=n\frac{\pi }{2}+(-1{)}^n\pi /12$ where n is integer