f(x)=2cos^2(x+π/6)+根号3*sin2x
=cos(2x+π/3)+1+√3sin2x
=cos2xcosπ/3-sin2xsinπ/3+1+√3sin2x
=√3/2sin2x+1/2cos2x+1
=sin(2x+π/6)+1
最大值为2
最小值为-1