Question

Solve the following equation:
$1+\sin x\cos 2x=\sin x+\cos 2x$

Answer 1

$1+\sin x\cos 2x=\sin x+\cos 2x$

$1+\sin x\cos 2x-\sin x-\cos 2x=0$

$(1-\sin x)-\cos 2x(1-\sin x)=0$

$(1-\sin x)(x-\cos 2x)=0$

Either, $1-\sin x=0,\sin x=1,x=2n\pi +\frac{\pi }{2}.$

or, $1-\cos 2x=0,\cos 2x=1,2x=2n\pi ,x=n\pi .$