-2cos2x=1 divide both sides by -2
cos2x = -1/2
Note......the cos (x) = -1/2 at x = 120° + n360° and at 240° + n360° where n is an integer
So......
2x = 120° +n 360° and at 240° + n360° divide both sides by 2
x = 60° + n180° and at 120° + n180° where n is an integer .....and this is the general solution