Sin (2x+п/2) = cos (x+п/2) + sin (x + п/2)

Sin (π/4 - x) * sin (π/4 - x/2) * sin (x/2) = 0Sin (2x+п/2) = cos (x+п/2) + sin (x + п/2) cos2x = - sinx + cosx

4sin (π/4 - x) * sin (π/4 - x/2) * sin (x/2) = 0

1) sin (π/4 - x) = 0

π/4 - x = πn, n∈Z

- x = πn - π/4, n∈Z

x1 = π/4 - πn, n∈Z

2) sin (π/4 - x/2) = 0

π/4 - x/2 = πk, k∈Z

- x/2 = πk - π/4, k∈Z

x2 = π/2 - 2πk, k∈Z

3) sin (x/2) = 0

(x / 2) = πm, m∈Z

x3 = 2πm, m∈Z

Ответ: x1 = π/4 - πn, n∈Z; x2 = π/2 - 2πk, k∈Z; x3 = 2πm, m∈Z