Solve cos(2x) = cos(x) for 0 <= x <= 2*pi.
cos (2x) = cos^2 - sin^2 or 2 cos^2 x -1
sooo 2 cos^2 x -1 = cos x
2 cos^2 x - cos x - 1 = 0 let x = cos x then use quadratic formula to find x = 1 or - 1/2
cos x = 1 or -1/2 then from 0 to 2pi this is 0 2 pi and 2pi/3 4pi/3