Cosx ≥ 0 - ОДЗ
2 + 2sin2x = (2cosx)²
2 + 2sin2x = 4cos²x
1 + sin2x = 2cos²x
sin²x + cos²x + sin2x = 2cos²x
sin²x - cos²x + sin2x = 0
-cos2x + sin2x = 0 | : cos2x, cos2x ≠ 0
sin2x/cos2x = 1
tg2x = 1
2x = π/4 + πk
x = π/8 + πk/2, k∈Z
чтобы удовлетворяла ОДЗ:
x = π/8 + 2πk
x = 13π/8+ 2πk, k∈Z