Cos 12 x*cos7x-cos4x*cos 15 x=0

1. Произведение косинусов:

2cosx * cosy = cos (x + y) + cos (x - y); cos12x * cos7x - cos4x * cos15x = 0; 2cos12x * cos7x - 2cos4x * cos15x = 0; cos (12x + 7x) + cos (12x - 7x) - (cos (15x + 4x) + cos (15x - 4x)) = 0; cos19x + cos5x - cos19x - cos11x = 0; cos5x - cos11x = 0.

2. Разность косинусов:

cosx - cosy = 2sin ((y + x) / 2) * sin ((y - x) / 2); 2sin ((11x + 5x) / 2) * sin ((11x - 5x) / 2) = 0; 2sin8x * sin3x = 0; [sin8x = 0;

[sin3x = 0; [8x = πk, k ∈ Z;

[3x = πk, k ∈ Z; [x = πk/8, k ∈ Z;

[x = πk/3, k ∈ Z.

Ответ: πk/8; πk/3, k ∈ Z.