f(x)=2cos方x-根号3倍的sin2x
=(1+cos2x)-√3sin2x
=1+2[cos2x*(1/2)-sin2x*(√3/2)]
=1+2[cos2xcos(π/3)-sin2x*sin(π/3)]
=1+2cos(2x+π/3)
(1)增区间
2kπ-π≤2x+π/3≤2kπ
∴ 2kπ-4π/3≤2x≤2kπ-π/3
∴ kπ-2π/3≤x≤kπ-π/6
∴ 增区间是【kπ-2π/3,kπ-π/6】,k∈Z
(2)减区间
2kπ≤2x+π/3≤2kπ+π
∴ 2kπ-π/3≤2x≤2kπ+2π/3
∴ kπ-π/6≤x≤kπ+π/3
∴ 减区间是【kπ-π/6,kπ+π/3】,k∈Z