f(x)＝2cos^2x＋根号3sin2x-2
=cos2x+1+√3sin2x-2
=2sin(2x+π/6)-1
f(π/3)=2sin(5π/6)-1=1-1=0
最小正周期为 2π/2=π
单调增区间：
2x+π/6∈[2kπ-π/2,2kπ+π/2]
x∈[kπ-π/3,kπ-π/6]
所以 单调增区间为 ∈[kπ-π/3,kπ-π/6] k∈z