f(x)=2cosxsin(x+π/3)=2cosx(1/2sinx+√3/2cosx)=1/2sin2x+√3/2(cos2x+1)
=sin(2x+π/3)+√3/2
-π/2<2x+π/3<π/2, -5π/12
x∈(0,π/2), f(π/12)=1+√3/2(最大值）f(π/2)=0
值域（0，1+√3/2】
