Y=6(cosx)^2-（2根号3）sinxcosx
=3×[2（cosx）^2-1]-根号3×2sinxcosx+3
=3cos2x-根号3×sin2x+3
=2根号3×（根号3/2×cos2x-1/2×sin2x）+3
=2根号3×（sin60°cos2x-cos60°sin2x）+3
=2根号3×sin（60°-2x）+3
所以T=2π/2=π.
答：Y的最小正周期为π