Cos4x+2cos квадрат x=1

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