Решить:

1-sin x/2=cos х

Решение

1-sin x/2=cos х

1 - sin x/2 = 1 - 2sin ² (x/2)

2sin ² (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