解f(x)=√3cosx+sinxcosx-√3/2 =√3*(1+cos2x)/2+(1/2)sin2x-√3/2 =(1/2)sin2x+(√3/2)cos2x =sin(2x+π/3) ∴T=π 单增区间：-π/2+2kπ≤2x+π/3≤π/2+2kπ,k∈Z -5π/6+2kπ≤2x≤π/6+2kπ,k∈Z -5π/12+kπ≤x≤π/12+2kπ,k∈Z 即为：[-π/12+kπ,5π/12+kπ],k∈Z