sin(x-π/6)cosx =sinxcosπ/6cosx-cosxsinπ/6cosx =√3/4sin2x-1/2(cosx)^2 =√3/4sin2x-1/4(1+cos2x) =√3/4sin2x-1/4cos2x-1/4 =1/2(√3/2sin2x-1/2cos2x)-1/4 =1/2sin(2x-π/6)-1/4