已知sina+cosa=根号3/3,则cos2a等于多少

sinα+cosα=√3/3
(sinα+cosα)²=1/3
sin²α+2sinαcosα+cos²α=1/3
1+sin2α=1/3
sin2α=-2/3＜0
cos2α=√(1-sin²2α)
=√[1-(-2/3)²]
=√(5/9)
cos2α=±√5/3