f(x)=sin∧2x+√3sinxcosx
=-1/2cos2x+√3/2sin2x-1/2=sin（2x-π/6）-1/2x∈［π/4,π/2］ 所以2x-π/6∈［π/3,5π/6］ 所以f（x）∈［0,1/2］即最大值为1/2