Решение
(sin x/2-cos x/2)²=1/2
sin² x/2 + 2sinx/2 * cosx/2 + cos² x/2 = 1/2
2sinx/2 * cosx/2 = 1/2 - 1
2sinx/2 * cosx/2 = - 1/2
sinx = - 1/2
x = (-1)^n * arcsin(-1/2) + πk, k ∈ Z
x = (-1)(n+1) * arcsin(1/2) + πk, k ∈ Z
x = (-1)(n+1) * (π/6) + πk, k ∈ Z