若tanα=√3,且α为第三象限角,则sinα-cosα=A.( -1-√3)/2 B.(-1+√3)/2 C.(1+√3)/2 D.(1-√3)/2

若tanα=√3,且α为第三象限角,则sinα-cosα=
A.( -1-√3)/2 B.(-1+√3)/2 C.(1+√3)/2 D.(1-√3)/2

由题意,可知α=4π/3,
则sinα-cosα=sin(4π/3)-cos(4π/3)=-√3/2-(-1/2)=(1-√3)/2
D