f(x)=2cosxsin(x+π／6)+2sinxcos(x+π／6)＝2sin(2x＋π/6)(1)∵x∈[0,π/2] ∴2x∈[0,π] ∴2x＋π/6∈[π/6,7π/6] ∴sin(2x＋π/6)∈[﹣1/2,1]∴f(x)的值域为：f(x)∈[﹣1,2](2)∵f(A)＝2sin(2A＋π/6)＝1 ∴sin...