f(x)＝(1+√3tanx)cosx＝cosx+√3sinx＝2sin(x+π/6).(1)最小正周期：T＝2π/1＝2π.(2)α∈(-π/6,π/3)→α+π/6∈(0,π/2).∴2sin(α+π/6)＝1/2→cos(α+π/6)＝√(1-1/16)＝√15/4.∴sinα＝sin[(α+π/6)-π/6...