Решить уравнение: sin^2 (x) - cos^2 (x) = cos (x/2)

Sin²x-cos²x=cos (x/2)

- (cos²x-sin²x) = cos (x/2)

-cos2x-cos (x/2) = 0

cosα+cosβ=2cos ((α+β) / 2) * cos ((α-β) / 2)

- (cos2x+cos (x/2)) = 0

2cos (5/4) x * cos (3/4) x=0

cos (5/4) x=0 или cos (3/4) x=0

1. cos (5/4) x=0

5/4x=π/2+πn, n∈Z

x₁=2π/5+4πn/5, n∈Z

2. cos (3/4) x=0

3/4x=π/2+πn, n∈Z

x₂=2π/3+4πn/3, n∈Z