(1)f(x)=2sin(x-π/3)cosx=sinxcosx-√3cos^2x=1/2sin2x-√3/2(1+cos2x)=sin(2x-π/3)-√3/2∴f(x)周期为T=2π/2=π。(2) f(x)单调增区间：2kπ-π/2<=2x-π/3<=2kπ+π/2==>kπ-π/12<=x<=kπ+5π/12∴f(x)在[0，5π/12]上单调递增，在[5π/12，π/2]上单调递减。
只有外星人才看得懂
