已知函数f(x)=4sinxcos(x+派/3)。(1)求f(x)最小正周期。(

解：(1)最简单的方法是用“积化和差”公式 2sinαcosβ = sin(α+β) + sin(α-β) 原式=2×2sinxcos(x+π/3) =2 [ sin(x+x+π/3) + sin(x-x-π/3) ] = 2 [ sin(2x + π/3) + sin (-π/3) ] = 2sin(2x + π/3) - √3