Решить уравнения:

1)

2)

1) 2cos5x + √3 = 0

2cos5x = - √3

cos5x = - √3/2

5x = ±5π/6 + 2πn, n ∈ Z

x = ±π/6 + 2πn/5, n ∈ Z

Ответ: x = ±π/6 + 2πn/5, n ∈ Z.

2) 4sin² (3π/2 + x) - 8sin (π/2 + x) = 0

4cos²x - 8cosx = 0

cos²x - 2cosx = 0

cosx (cosx - 2) = 0

cosx = 0

x = π/2 + πn, n ∈ Z

cosx - 2 = 0

cosx = 2 - нет корней, т. к. cosx ∈ [-1; 1]

Ответ: x = π/2 + πn, n ∈ Z.