sinα-√3cosα
=2*[sinα*(1/2)-cosα*(√3/2)]
=2[sinαcos(π/3)-cosαsin(π/3)]
=2sin(α-π/3)
要使sinα-根號(hào)3cosα=4m-6對(duì)a∈R都有意義
即 2sin(α-π/3)=4m-6對(duì)a∈R都有意義
函數(shù)y=2sin(α-π/3)的值域是[-2,2]
∴ 4m-6∈[-2,2]
∴ -2≤4m-6≤2
∴ 4≤4m≤8
∴ 1≤m≤2
即實(shí)數(shù)m的取值范圍是[1,2]