Подробное решение
sin^2(2x-1)=1/2

Sin^2(2x-1)=1/2а) Sin(2x -1) = 1/√2, ⇒ 2х -1 = (-1)ⁿ π/4 + nπ, n ∈Z2x = 1 +(-1)ⁿ π/4 + nπ, n ∈Zx = 1/2 +(-1)ⁿ π/8+ nπ/2, n ∈Z б)Sin(2x -1) = - 1/√2, ⇒ 2х -1 = (-1)ⁿ⁺¹ π/4 + nπ, n ∈Z2x = 1 +(-1)ⁿ⁺¹ π/4 + nπ, n ∈Zx = 1/2 +(-1)ⁿ⁺¹ π/8+ nπ/2, n ∈Z