求函数y=2cosxsinx(x+π/3)-根号3sin^2x+sinxcosx的周期，最值和单调区间
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y=2cosxsinx(x+π/3)-根号3sin^2x+sinxcosx
=2cosx[1/2*sinx+√3/2*cosx]-√3sin^2x+sinxcosx
=sinxcosx+√3cos^2x-√3sin^2x+sinxcosx
=2sinxcosx+√3[cos^2x-sin^2x]
=sin2x+√3cos2x
=2(1/2sin2x+√3/2*cos2x)
=2sin(2x+π/3)
周期：π
最值：±2
单调区间：[-5π/12+2kπ，π/12+2kπ] 单调增
（π/12+2kπ，7π/12+2kπ]）单调减
=2cosx[1/2*sinx+√3/2*cosx]-√3sin^2x+sinxcosx
=sinxcosx+√3cos^2x-√3sin^2x+sinxcosx
=2sinxcosx+√3[cos^2x-sin^2x]
=sin2x+√3cos2x
=2(1/2sin2x+√3/2*cos2x)
=2sin(2x+π/3)
周期：π
最值：±2
单调区间：[-5π/12+2kπ，π/12+2kπ] 单调增
（π/12+2kπ，7π/12+2kπ]）单调减
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