f(x)=2sinxcos(x＋π/3)＋√3/2=2sinx(1/2cosx-√3/2sinx)＋√3/2=1/2*2cosx-√3/2*2(sinx)^2＋√3/2=1/2sin2x-√3/2(1-cos2x)＋√3/2=1/2sin2x+√3/2cos2x=sin(2x+π/3)因:2x+π/3∈[2kπ+π/2,2kπ+3π/2]是单调递减所以:x∈[kπ+π/12,kπ+7π/12]是单调递减
