2*sin (2x + 6x)/2 *cos (2x - 6x)/2 = 2*sin (x + 5x)/2 * cos (x - 5x)/2
2 sin (8x )/2 cos 2x = 2sin (6x)/2 * cos 2x
2 sin4x cos2x - 2sin 3x cos2x = 0 /:2
sin4x cos2x - sin3x cos2x = 0
cos2x (sinx4x - sin3x) = 0
1) cos2x = 0
2x = pi/2 + pik /:2
x = pi/4 + (pik)/2, k ∈ Z
2) sin4x - sin3x = 0
2 sin (4x - 3x)/2 cos (4x + 3x)/2 = 0
2 sin x/2 cos 7x/2 = 0 /:2
sin (x/2) * cos (7x/2) = 0
2.1
sin x/2 = 0
x/2 = pik /*2
x = 2pik, k ∈Z
2.2
cos (7x/2) = 0
(7x)/2 = pi/2 + pik / * 2/7
x = pi/7 + (2pik)/7, k ∈Z
Ответ
x = pi/4 + (pik)/2, k ∈ Z
x = 2pik, k ∈Z
x = pi/7 + (2pik)/7, k ∈Z