Question

已知sina+cosa=1/3,则cos2a=

Answer 1

由：sina+cosa=1/3,

得：(sina+cosa)^2=(1/3)^2

(sina)^2+2sinacosa+(cosa)^2=1/9

1+2sinacosa=1/9

sin2a=-8/9

因为：(sin2a)^2+(cos2a)^2=1

所以：cos2a=±√[1-(-8/9)^2]=±√(17/81)=±√17/9