1) cos7x + cosx=02) sin²x - 3sinxcosx+2cos²x=03) 1+cosx+cos2x=0

1. Сумма косинусов:

cos7x + cosx = 0; 2cos ((7x + x) / 2) * cos ((7x - x) / 2) = 0; 2cos4x * cos3x = 0; [cos4x = 0;

[cos3x = 0; [4x = π/2 + πk, k ∈ Z;

[3x = π/2 + πk, k ∈ Z; [x = π/8 + πk/4, k ∈ Z;

[x = π/6 + πk/3, k ∈ Z.

2.

sin^2x - 3sinx * cosx + 2cos^2x = 0; tg^2x - 3tgx + 2 = 0; D = 3^2 - 4 * 2 = 1; tgx = (3 ± 1) / 2;

1) tgx = (3 - 1) / 2 = 1;

x = π/4 + πk, k ∈ Z.

2) tgx = (3 + 1) / 2 = 2;

x = arctg2 + πk, k ∈ Z.

3.

1 + cosx + cos2x = 0; cosx + 2cos^2x = 0; cosx (1 + 2cosx) = 0; [cosx = 0;

[1 + 2cosx = 0; [cosx = 0;

[cosx = - 1/2; [x = π/2 + πk, k ∈ Z;

[x = ±2π/3 + 2πk, k ∈ Z.