y=2√3 sinxcosx-2sin^2x的单调区间

题目

y=2√3 sinxcosx-2sin^2x的单调区间

答案

y=2√3 sinxcosx-2sin^2x
=√3 sin2x-1+cos2x
=2(√3/2 sin2x+1/2cos2x)-1
=2sin(2x+π/6)-1
x在[kπ-π/3,kπ+π/6]单调递增
x在[kπ+π/6,kπ+4π/3]单调递减