2sin(x/2-p/6)=-1. Помогите плизззззз

Question

2sin(x/2-p/6)=-1. Помогите плизззззз

Answer 1

2sin(x/2-π/6)=-1
sin(x/2-π/6)=-1/2
x/2-π/6=(-1)^(k+1) π/6+πk, k∈Z
x/2=(-1)^(k+1) π/6+πk+π/6, k∈Z
x/2=(-1)^(k+1) π/3+πk, k∈Z
x=(-1)^(k+1) 2π/3+2πk, k∈Z
ответ: x=(-1)^(k+1) 2π/3+2πk, k∈Z