y=2根号3sinxcosx-2cos^2x+1
＝根号3sin2x-cos2x
=2sin(2x-π/6)
T=2π/2=π
2x-π/6=2kπ+π/2
当x=kπ+π/3时,函数的最大值=2
2x-π/6=2kπ+3π/2
当x=kπ+5π/6时,最小值=-2