Cosx+(корень из 3)*sinx=sin(x/2-пи/6)

2(1/2*сosx+√3/2*sinx)=sin(x/2-π/6)
2сos(x-π/3)=sin(x/2-π/6)
x-π/3=2*(x/2-π/6)
2*(1-2sin²(x/2-π/6))-sin(x/2-π/6)=0
sin(x/2-π/6)=a
2-4a²-a=0
4a²+a-2=0
D=1+32=33
a1=(-1-√33)/8
sin(x/2-π/6)=(-1-√33)/8
x/2-π/6=(-1)^(n+1)acrsin[(1+√33)/8]+πn
x/2=π/6+(-1)^(n+1)acrsin[(1+√33)/8]+πn
x=π/3+(-1)^(n+1)*2acrsin[(1+√33)/8]+2πn,n∈z
a1=(-1+√33)/8
sin(x/2-π/6)=(-1+√33)/8
x/2-π/6=(-1)^k*acrsin[(-1+√33)/8]+πk
x/2=π/6+(-1)^*acrsin[(-1+√33)/8]+πk
x=π/3+(-1)^k*2acrsin[(-1+√33)/8]+2πk,k∈z