Подробное решение sin^2(2x-1)=1/2

Question

Подробное решение
sin^2(2x-1)=1/2

Answer 1

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