Sin15x * sin3x+cos7x*cos11x=0

1/2 (cos (15x - 3x) - cos (15x + 3x)) + 1/2 (cos (7x - 11x) + cos (7x + 11x)) = 0

1/2 cos12x - 1/2 cos18x + 1/2 cos4x + 1/2 cos18x = 0

cos12x + cos4x = 0

2cos ((12x + 4x) / 2) ·cos ((12x - 4x) / 2) = 0

cos8x = 0 или cos4x = 0

8x = π/2 + πn 4x = π/2 + πk

x = π/16 + πn/8 x = π/8 + πk/4

sin15x*sin3x+cos7x*cos11x=0

2cos (12x) - 1/2cos (4x) = 0

2*sin (12x + 4x) / 2sin (4x - 12x) / 2 = 0

sin (8x) = 0

8cos=πn, n∈X

8x = (πn) / 8, n∈Z

8x = (пи/4) = 0

Ответ:πn/16+πn/8 и πn/4+πn/8