f(x)=1+cos2x-√3sin2x=1-2sin(2x-π/6)
∴最小正周期T=2π/2=π
∵2kπ-π/2≤2x-π/6≤2kπ+π/2
∴单调减区间x∈[kπ-π/6,kπ+π/3]