y
=2√3sinxcosx+2cos^2(x)-1
=√3(2sinxcosx)+2*[1+cos2x]/2-1
=√3sin2x+cos2x
=2sin(2x+π/6)
(辅助角公式)
设T=2x+π/6
则:2sin(2x+π/6)的单调增区间为:
2kπ-π/2