√3*sin(x/2)+1=cosx
cosx=cos(2*(x/2))=cos²(x/2)-sin²(x/2)=1-2sin²(x/2)
√3*sin(x/2)+1=1-2sin²(x/2)
2sin²(x/2)+√3*sin(x/2)=0
sin(x/2)*(2sin(x/2)+√3)=0
sin(x/2)=0 или 2sin(x/2)+√3=0
1. sin(x/2)=0 частный случай.
x/2=π/2+2πn, n∉Z |*2
x₁=π+4πn, n∈Z
2. 2sin(x/2)+√3=0
sin(x/2)=-√3/2
x/2=(-1)^n *arcsin(-√3/2)+πn, n∈Z
x/2=(-1)^(n+1) *(π/3)+πn, n∈Z |*2
x₂=(-1)^(n+1) *(2π/3)+2πn, n∈Z