Question

Find the solution of cos(x)-1=2sin^2(x) on interval [0,2π)

Answer 1

Transform the trig equation so that it only has cos x as invariable (x = cos x).
Replace 2 sin^2x by (2 - 2cos^2 x). The equation results in:
2cos^2x + cos x -3 = 0. It is a quadratic equation in x = cos x. Solve to get x = cos x. Reject answer outside (-1, 1).