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.