find all solutions of the equation

Question

sin (2x)sin (x)-cos (2x)cos (x)=-cos (x)

Answer 1

The LHS is -cos 3x.

Graph -cos 3x + cos x

You will see that the function is periodic with period 2π.and it, like cos is an even function

The roots between -π and π are -π, π -π/2 and π/2,