f(x)=cos²x-√3sinxcosx+1
=1/2[cos(2x)+1]-√3/2sin(2x)+1
=1/2cos(2x)-√3/2sin(2x)+3/2
=cos(2x+π/3)+3/2
1）2kπ+π≤2x+π/3≤2kπ+2π
kπ+π/3≤x≤kπ+5π/6
单增区间：[kπ+π/3,kπ+5π/6] (k∈Z)