1.f(x)=cos^2(x/2)+√3sin(x/2)cos(x/2)+a=(1/2)(cosx+1)+(√3/2)sinx+a
=(√3/2)sinx+(1/2)cosx+1/2+a=sin(x+π/6)+1/2+a
点（π/3,2)代入,sin(π/3+π/6)+1/2+a=2,a=1/2
2.f(x)=sin(x+π/6)+1,最小正周期=2π,
当0≤x≤π时,π/6≤x+π/6≤7π/6,-1/2≤sin(x+π/6)≤1,
1/2≤sin(x+π/6)+1≤2,所以值域为[1/2,2]