Решить: 1-sin x/2=cos х

Решение 1-sin x/2=cos х 1 - sin x/2 = 1 - 2sin²(x/2) 2sin²(x/2) - sin(x/2) = 0 sin(x/2) * (2sin(x/2) - 1) = 0 1)  sin(x/2) = 0 x/2 = πk, k ∈Z x₁ = 2πk, k ∈ Z 2)  2sin(x/2) - 1 = 0 2sin(x/2)  =  1 sin(x/2) = 1/2 x/2 = (-1)^n * arcsin(1/2) + πn, n ∈Z x/2 = (-1)^n * (π/6) + πn, n ∈Z x₂ = (-1)^n * (π/3) + 2πn, n ∈Z Ответ: x₁ = 2πk, k ∈ Z ; x₂ = (-1)^n * (π/3) + 2πn, n ∈Z