Cos (4x) + 8sin^2 (x) - 2=6cos (2x) - 8cos^4 (x)

Cos (4x) + 8sin^2 x - 2 = 6cos (2x) - 8cos^4 x

2cos^2 (2x) - 1 + 8 (1 - cos^2 x) - 2 = 6 (2cos^2 x - 1) - 8cos^4 x

2 (2cos^2 x - 1) ^2 - 1 + 8 - 8cos^2 x - 2 = 12cos^2 x - 6 - 8cos^4 x

2 (4cos^4 x - 4cos^2 x + 1) + 11 - 8cos^2 x = 12cos^2 x - 8cos^4 x

8cos^4 x - 8cos^2 x + 2 + 11 - 8cos^2 x = 12cos^2 x - 8cos^4 x

16cos^4 x - 28cos^2 x + 11 = 0

Квадратное уравнение относительно cos^2 x

D/4 = 14^2 - 16*11 = 196 - 176 = 20

cos^2 x = (14 - √20) / 16 = (14 - 2√5) / 16 = (7 - √5) / 8 ~ 0,5955

cos^2 x = (14 + √20) / 16 = (14 + 2√5) / 16 = (7 + √5) / 8 ~ 1,15 > 1 - решений нет

cos x1 = - √ ((7 - √5) / 8)

cos x2 = √ ((7 - √5) / 8)