Cosx + (корень из 3) * sinx=sin (x/2-пи/6)

2 (1/2*сosx+√3/2*sinx) = sin (x/2-п/6)

2 сos (x-п/3) = sin (x/2-п/6)

x-п/3=2 * (x/2-п/6)

2 * (1-2sinп (x/2-п/6)) - sin (x/2-п/6) = 0

sin (x/2-п/6) = a

2-4a2-a=0

4aп+a-2=0

D=1+32=33

a1 = (-1-√33) / 8

sin (x/2-п/6) = (-1-√33) / 8

x/2-п/6 = (-1) ^ (n+1) acrsin[ (1+√33) / 8]+пn

x/2=п/6 + (-1) ^ (n+1) acrsin[ (1+√33) / 8]+пn

x=п/3 + (-1) ^ (n+1) * 2acrsin[ (1+√33) / 8]+2 пn, n∈z

a1 = (-1+√33) / 8

sin (x/2-п/6) = (-1+√33) / 8

x/2-п/6 = (-1) ^k*acrsin[ (-1+√33) / 8]+пk

x/2=п/6 + (-1) ^*acrsin[ (-1+√33) / 8]+пk

x=п/3 + (-1) ^k*2acrsin[ (-1+√33) / 8]+2 пk, k∈z

вот и всё.