y =sin2x+2根号3sinxsinx
=sin2x+2根号3sin^2x
=sin2x+根号3(1-cos2x)
=sin2x-根号3cos2x+根号3
=2(1/2sin2x-根号3/2cos2x)+根号3
=2sin(2x-60)+根号3
T=2π/2=π
最大值为=2+根号3