f(x)=cos2x - 根号3sinxcosx +1
=cos2x - 2分之根号3sin2x +1
=cos(2x+π/3)+1
令2kπ-π≤2x+π/3≤2kπ
∴kπ-2π/3≤x≤kπ-π/6
∴f(x)的增区间是[kπ-2π/3,kπ-π/6]