y=0.5(1-cos2x)/2+√ 3/4sin2x+1=√ 3/4sin2x-1/4 cos2x+5/4=1/2(√ 3/2sinx-1/2 cosx)+5/4=1/2sin(x-π/6)+5/4.所以最大值为7/4.此时x=2π/3+2kπ.k∈Z