4cos²x + sinx - 1 = 0
4 - 4sin²x + sinx - 1 = 0
-4sin²x + sinx + 3 = 0
4sin²x - sinx - 3 = 0
4sin²x - 4sinx + 3sinx - 3 = 0
4sinx(sinx - 1) + 3(sinx - 1) = 0
(4sinx + 3)(sinx - 1) = 0
1) 4sinx + 3 = 0
sinx = -3/4
x = (-1)ⁿ⁺¹arcsin(3/4) + πn, n ∈ Z
2) sinx - 1 = 0
sinx = 1
x = π/2 + 2πk, k ∈ Z
Ответ: x = (-1)ⁿ⁺¹arcsin(3/4) + πn, n ∈ Z; π/2 + 2πk, k ∈ Z.