∵f（x）=2√3cos² x+2sinxcosx-√3
=√3(1+cos2x)+sin2x-√3
=√3cos2x+sin2x
=2sin(2x+π/3)
（1）∴.f（x）的最小正周期T=2π/2=π
(2)由2kπ-π/2=≤2x+π/3≤2kπ+π/2,
即kπ-5π/12≤x≤kπ+π/12
由 2kπ+π/2≤2x+π/3≤2kπ+3π/2,即kπ+π/12≤x≤kπ+7π/12 ；
∴.f（x）的单调增间为：[kπ-5π/12,kπ+π/12]
单调减区间为：[kπ+π/12,kπ+7π/12];k∈Z