Question

sin2x=sin(π/2+x) помогите решить тригонометрическое уравнение

Answer 1

sin2x = sin(π/2+x)
2sinxcosx = cosx
2sinxcosx - cosx = 0
cosx(2sinx - 1) = 0
1) cosx = 0
x = π/2 + πn , n∈Z
2) 2sinx - 1 = 0
sinx = 1/2
x = (-1)^n* π/4+ πn, n∈Z
Ответ: x = π/2 + πn , n∈Z  и  x = (-1)^n* π/4+ πn, n∈Z