已知tanα=√3
所以α=kπ+π/3
因为π＜α＜3π/2
所以α=π+π/3=4π/3

所以sinα-cosα=sin(4π/3)-cos(4π/3)=-sin(π/3)+cos(π/3)=-√3/2+1/2=(1-√3)/2
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