Solve Sinx=Cos2x-1 for all values between 0 and 2pi

Answer 1

cos 2x = 1 - 2sin^2 x
so, you have

2sin^2 x + sin x = 0
sin x (2sin x + 1) = 0
sinx = 0 --> x = 0,2pi
sinx = -1/2 --> x = 7pi/6,11pi/6