已知函数f（x）=根号三cos²x+sinxcosx-根号三/2

f（x）=√3cos²x+sinxcosx-√3/2
=√3(cos2x+1)/2+sin2x /2-√3/2
=√3/2cos2x+√3/2+1/2sin2x -√3/2
=1/2sin2x+√3/2cos2x
=sin(2x+π/3)
（1）最小正周期为
T=2π/w=2π/2=π
（2）单调递增区间
2kπ-π/2≤2x+π/3≤2kπ+π/2 （k∈Z）
2kπ-π/2-π/3≤2x≤2kπ+π/2-π/3
2kπ-5π/6≤2x≤2kπ+π/6
kπ-5π/12≤x≤kπ+π/12
即单调递增区间为[kπ-5π/12,kπ+π/12] （k∈Z）