2sin²(x/2) = cos(3π/2 + x/2)
2sin²(x/2) = cos(π + π/2 + x/2)
2sin²(x/2) = sin(x/2)
2sin²(x/2) - sin(x/2) = 0
sin(x/2)[2sin(x/2) - 1) = 0
1) sin(x/2) = 0
x/2 = πn, n ∈ Z
x = 2πn, n ∈ Z
2) 2sin(x/2) - 1 = 0
sin(x/2) = 1/2
x/2 = (-1)ⁿπ/6 + πk, k ∈ Z
x = (-1)ⁿπ/3 + 2πk, k ∈ Z
Ответ: x = 2πn, n ∈ Z; (-1)ⁿπ/3 + 2πk, k ∈ Z.