1) sin x * cos2x - cos x * sin2x = 1/2 2) 2cos - sin x * cos x = 0 3) 2 (cosx) ^2 - cosx - 1 = 0

1) Синус разности:

sinx * cos2x - cosx * sin2x = 1/2; sin (x - 2x) = 1/2; sin (-x) = 1/2; - sinx = 1/2; sinx = - 1/2; [x = - π/6 + 2πk, k ∈ Z;

[x = - 5π/6 + 2πk, k ∈ Z.

2) Общий множитель:

2cosx - sinx * cosx = 0; cosx (2 - sinx) = 0; [cosx = 0;

[2 - sinx = 0; [x = π/2 + πk, k ∈ Z;

[sinx = 2 > 1 - нет решения; x = π/2 + πk, k ∈ Z.

3) Квадратное уравнение:

2cos^2x - cosx - 1 = 0; D = 1^2 + 4 * 2 = 9; cosx = (1 ± √9) / 4 = (1 ± 3) / 4;

a) cosx = (1 - 3) / 4 = - 2/4 = - 1/2;

x = ±2π/3 + 2πk, k ∈ Z.

b) cosx = (1 + 3) / 4 = 4/4 = 1;

x = 2πk, k ∈ Z.