已知向量a=(cosα,sinα)向量b=(cosβ,sinβ)则|a-b|的取值范围为

向量a-b=(cosα-cosβ,sinα-sinβ),
|a-b|=√[（cosα-cosβ）^2+(sinα-sinβ)^2]
=√[（cosα)^2+(sinα)^2+(cosβ)^2+(sinβ)^2-2cosαcosβ-2sinαsinβ]
=√[2-2cos(α-β)]
-2