Question

Find all solutions to the equation in the interval [0, 2π). (1 point) cos x = sin 2x

Answer 1

Cos x = sin 2x
cos x = 2 sin x cosx

2sin x cos - cos x = 0

cos x( 2 sin x - 1) = 0

cos x = 0 or sin x = 1/2

so required values of x are pi/6 , 5pi/6 ,   pi/2,  3pi/2.