1 + sinx = 2cos²x
1 - 2cos²x + sinx = 0
2 - 2cos²x + sinx - 1 = 0
2sin²x + sinx - 1 = 0
Пусть t = sinx, t ∈ [-1; 1]
2t² + t - 1 = 0
D = 1 + 8 = 9 = 3²
t1 = (-1 + 3)/4 = 1/2
t2 = (-1 - 3)/4 = -1
Обратная замена:
sinx = 1/2
x = (-1)ⁿπ/6 + πn, n ∈ Z
sinx = -1
x = -π/2 + 2πn, n ∈ Z