若π/4≤π≤π/3,则函数y=[2sin（x+π/6）]/cosx的值域是多少?

y=2(sinxcosπ/6+cosxsinπ/6)/cosx
=2sinxcosπ/6/cosx+2cosxsinπ/6/cosx
=√3tanx+1
π/4≤x≤π/3
tanπ/4≤tanx≤tanπ/3
√3≤√3tanx≤3
√3+1≤√3tanx+1≤4
值域[√3+1,4]