Замена cos x = t
8t^4 - 8t^2 - t + 1 = 0
8t^2*(t^2 - 1) - (t - 1) = 0
8t^2*(t - 1)(t + 1) - (t - 1) = 0
(t - 1)(8t^2(t + 1) - 1) = 0
t1 = cos x = 1; x1 = 2pi*k
8t^3 + 8t^2 - 1 = 0
8t^3 + 4t^2 + 4t^2 + 2t - 2t - 1 = 0
(2t + 1)(4t^2 + 2t - 1) = 0
t2 = cos x = -1/2; x2 = +-2pi/3 + 2pi*n
Решаем квадратное уравнение
4t^2 + 2t - 1 = 0
D/4 = 1 + 4*1 = 5
t3 = cos x = (-1 - √5)/4; x3 = +-arccos(
(-1 - √5)/4
) + 2pi*m
t4 = cos x = (-1 + √5)/4; x4 = +-arccos(
(-1 + √5)/4
) + 2pi*q