Cos 9 x - cos 7 x + cos 3 x - cos x = 0

Cos (9x) - cos (7x) + cos (3x) - cos (x) = 0.

Решение:

(cos 9x - cos x) = (cos 7x - cos 3x)

- 2 sin [ (9x+x) / 2] * sin [ (9x-x) / 2] = - 2 sin [ (7x+3x) / 2] * sin [ (7x-3x) / 2]

sin 5x * sin 4x = sin 5x * sin 2x

sin 4x = sin 2x

2 sin 2x * cos 2x = sin 2x

2 cos 2x = 1

cos 2x = 1/2

2x = п/3 = 60 град.

x = 60/2 = 30 град.