函数y=1/2sin(2X+TT/3)-sinXcosX的单调递减区间是
问题描述：
函数y=1/2sin(2X+TT/3)-sinXcosX的单调递减区间是
答
y=1/2sin(2X+TT/3)-sinXcosX
=1/2sin2x*1/2 +1/2cos2xsinπ/3 -1/2sin2x
=-1/4sin2x+1/2cos2xsinπ/3
=1/2(cos2xsinπ/3-sin2xcosπ/3)
=1/2sin(π/3-2x)
=-1/2sin(2x-π/3)
单调减区间是
2kπkπ+π/6
答
y=1/2sin(2X+TT/3)-sinXcosX
=cos(2x+TT/6)sin(TT/6)
=1/2cos(2x+TT/6)
单调递减区间是2kπ≤2x+π/6≤2kπ+π
kπ-π/12≤x≤kπ+5π/12