Решите уравнение: cos5x+cos3x=0; cos7x-cos5x=0; sin9x-sin13x=0.

1. Сумма косинусов:

cos5x + cos3x = 0; 2cos4x * cosx = 0; [cos4x = 0;

[cosx = 0; [4x = π/2 + πk, k ∈ Z;

[x = π/2 + πk, k ∈ Z; [x = π/8 + πk/4, k ∈ Z;

[x = π/2 + πk, k ∈ Z.

2. Разность косинусов:

cos7x - cos5x = 0; - 2sin6x * sinx = 0; sin6x * sinx = 0; [sin6x = 0;

[sinx = 0; [6x = πk, k ∈ Z;

[x = πk, k ∈ Z; [x = πk/6, k ∈ Z;

[x = πk, k ∈ Z.

3. Разность синусов:

sin9x - sin13x = 0; sin13x - sin9x = 0; 2sin2x * cos11x = 0; [2x = πk, k ∈ Z;

[11x = π/2 + πk, k ∈ Z; [x = πk/2, k ∈ Z;

[x = π/22 + πk/11, k ∈ Z.