y=sin2x+√3cos2x
=2sin(2x+π/3)
单调增区间：
令2kπ-π/2＜2x+π/3＜2kπ+π/2,k∈Z
得kπ-5π/12＜x＜kπ+π/12,k∈Z
所以函数的单调增区间是(kπ-5π/12,kπ+π/12),k∈Z
单调减区间：
令2kπ+π/2＜2x+π/3＜2kπ+3π/2,k∈Z
得kπ+π/12＜x＜kπ+7π/12,k∈Z所以函数的单调减区间是(kπ+π/12,kπ+7π/12),k∈Z