f（x）＝2cos²x+√3sin2x
=cos2x+√3sin2x +1
=2(√3/2sin2x+cos2x )+1
=2sin(2x+π/6)+1
2x+π/6在[2kπ-π/2,2kπ+π/2]上单调递增
x在[kπ-π/3,kπ+π/6]上单调递增