Формула cos 2a = 2cos^2 a - 1
cos 4x = 1 - 2cos^2 x = -cos 2x
2cos^2 (2x) - 1 = -cos 2x
Замена cos 2x = y
2y^2 - 1 = -y
2y^2 + y - 1 = 0
(y + 1)(2y - 1) = 0
1) y = cos 2x = -1; 2x = pi + 2pi*k; x1 = pi/2 + pi*k
2) y = cos 2x = 1/2; 2x = +-pi/3 + 2pi*n; x2 = +-pi/6 + pi*n