f(x)=4cos^2x-4√3sinxcosx-1
=8cosx（1/2cosx-√3/2sinx）-1
=8cosx（sinπ/6cosx-cosπ/6sinx）-1
=8cosxsin（π/6-x）-1
=4（sinπ/6-sin（2x-π/6）-1
=2-4sin（2x-π/6）-1
=1-4sin（2x-π/6）
（1）最小正周期T=2π/ω=π
（2）单调递增区间
2Kπ+π/2≤2x-π/6≤2Kπ+3π/2
2Kπ+2π/3≤2x≤2Kπ+5π/3
Kπ+π/3≤x≤Kπ+5π/6
（3）2x-π/6=Kπ+π/2
2x=Kπ+2π/3
x=Kπ/2+π/3
对称轴为x=Kπ/2+π/3