Find all values of x in the interval [0, 2π] that satisfy the equation. (enter your answers as a comma-separated list.) 6 sin (2x) = 6 cos (x)

6 sin 2x = 6 cos x Using the identity sin 2x = 2 sin x cos x:-

12 sin x cos x = 6 cos x

6 cos x (2 sin x - 1) = 0

either 6 cos x = 0 or 2 sin x - 1 = 0 so sin x = 1/2

x = pi/2, 3pi/2, pi/6, 5pi / 6

answer is (pi/6, pi/2, 5pi/6, 2pi/2)