1) Cos2x=0,1 2) 2cos²x=1 3) sin4x=-1

Решите уравнения:

1) cos (2x) = 0,1; 2) 2cos²x = 1; 3) sin (4x) = - 1.

Решение.

1) cos (2x) = 0;

2x = π/2 ± πk;

x = π/4 ± πk/2, k ∈ Z.

2) 2cos²x = 1;

cos²x = 1/2;

cosx = ± √2/2;

x = π/4 ± 2πk; 3π/4 ± 2πk, k ∈ Z.

3) sin (4x) = - 1;

4x = - π/2 ± 2πk;

4x = - π/8 ± πk/2, k ∈ Z.

Ответ: 1) π/4 ± πk/2; 2) π/4 ± 2πk; 3π/4 ± 2πk; 3) - π/8 ± πk/2, k ∈ Z.