已知α为第二象限角,sinα+cosα=根号3/3,则cos2α=

sinα+cosα=√3/3
(sinα+cosα)^2=1/3
2sinacosa=1/3-1=-2/3
sinα-cosα>0,
(sinα-cosα)^2=1-2sinacosa=5/3
sinα-cosα=√(5/3)
cos2α=-(sinα-cosα))(sinα+cosα)=-√(5/3) * (√3/3)=-(√5)/3