f(x)=[1+sinx-2sin²(π/4-x/2)]/4*(sinx/2)+√3（sinx/2）
=[1+sinx-1+cos(π/2-x)]/4(sinx/2)+√3（sinx/2）
=sinx/2sin(x/2)+√3（sinx/2)
=2sin(x/2)cos(x/2)/2sin(x/2)+√3（sinx/2)
=cos(x/2)+√3（sinx/2)
=2sin(x/2+π/6)
当(x/2+π/6)∈{2kπ+π/2},即x∈{4kπ+2π/3}时,得最大值2