ac=b^2=a^2+c^2-2accosx
==> ac(1+2cosx)=a^2+c^2≥2ac
==> cosx≥1/2
==> 0＜x≤π/3
f(x)=sinx/3cosx/3+√3(cosx/3)^2
=(1/2)sin2x/3+(√3/2)(1+cos2x/3)
=sin(2x/3+π/3)+√3/2
0＜x≤π/3 ==> π/3＜2x/3+π/3≤5π/9
==> √3/2＜sin(2x/3+π/3)≤1
==> √3＜f(x)≤1+√3/2
所以f(x)的值域是（√3,1+√3/2]