2sin(x/2-pi/6)=-1 помогите пожалуйста

Question

2sin(x/2-pi/6)=-1 помогите пожалуйста

Answer 1

Решение
2sin(x/2 - π/6) = - 1
sin(x/2 - π/6) = - 1/2
x/2 - π/6 = (-1)^(n)*arcsin(-1/2) + πn. n∈Z
x/2 - π/6 = (-1)^(n+1)*arcsin(1/2) + πn. n∈Z
x/2 - π/6 = (-1)^(n+1)*(π/6) + πn. n∈Z
x/2  = (-1)^(n+1)*(π/6) + π/6 + πn. n∈Z
x  = (-1)^(n+1)*(π/3) + π/3 + 2πn. n∈Z