Решите уравнение 2sinxcosx-cosx^2x/2=sin^2x/2

Question

Решите уравнение 2sinxcosx-cosx^2x/2=sin^2x/2

Answer 1

2sinxcosx - cos²(x/2) = sin²(x/2)
sin2x = sin²(x/2) + cos²(x/2)
sin2x = 1
2x = π/2 + 2πn, n ∈ Z
x = π/4 + πn, n ∈ Z
Ответ: x = π/4 + πn, n ∈ Z.