⑴f(x)＝2sin(π－x)cosx＝2sinxcosx＝sin2x
最小正周期T＝2π/2＝π
⑵∵x∈[－π/6,π/2]
∴2x∈[－π/3,π]
∴f(x)max＝sin(π/2)＝1,f(x)min＝sin(－π/3)＝－1/2.