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.