f(x)=(sinx)^2+√3sinxcosx =(√3/2)sin2x-(1/2)cos2x+1/2 =sin2xcosπ/6-cos2xsinπ/6+1/2 =sin(2x-π/6)+1/2 π/4<=x<=π/2，则π/3<=2x-π/6<=5π/6 当2x-π/6=π/2、即x=π/3时，f(x)取得最大值f(π/3)=1+1/2=3/2.
