sina-√3cosa
=2*[sina*(1/2)-cosa*(√3/2)]
=2[sinacos(π/3)-cosasin(π/3)]
=2sin(a-π/3)
要使sina-根号3cosa=4m-6对a∈R都有意义
即 2sin(a-π/3)=4m-6对a∈R都有意义
函数y=2sin(a-π/3)的值域是[-2,2]
∴ 4m-6∈[-2,2]
∴ -2≤4m-6≤2
∴ 4≤4m≤8
∴ 1≤m≤2
即实数m的取值范围是[1,2]