Question

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

Answer 1

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