Find the x-coordinates of all points on the curve

Question

f(x) = sin 2x − 2 sin x
at which the tangent line is horizontal. (Enter your answers as a comma-separated list. Use n to represent any integer.)

Answer 1

tangent is horizontal when f'(x) = 0

f'(x) = 2cos2x - 2cosx
f'(x) = 0 when x = 2k*pi or 2k*pi +/- 2pi/3
for all integers k