1 - cosx - sin x/2 = 0

Решение

1 - cosx - sin x/2 = 0

1 - (1 - 2sin²x/2) - sinx/2 = 0

1 - 1 + 2sin²x/2 - sinx/2 = 0

2sin²x/2 - sinx/2 = 0

sinx/2 (2sinx/2 - 1) = 0

1) sinx/2 = 0

x/2 = πk, k∈Z

x₁ = 2πk, k∈Z

2) 2sinx/2 - 1 = 0

sinx/2 = 1/2

x/2 = (-1) ^narcsin (1/2) + πn, n∈Z

x/2 = (-1) ^n (π/6) + πn, n∈Z

x₂ = (-1) ^n (π/3) + πn, n∈Z

Ответ: x₁ = 2πk, k∈Z; x₂ = (-1) ^n (π/3) + πn, n∈Z