cosα/2+sinα/2=-根号5/2 (cosα/2+sinα/2)^2=5/4
1+sinα=5/4 sinα=1/4 (sinα/2-cosα/2)^2=1-sinsinα3/4
sinα/2-cosα/2=根号3/2
sinα=1/4 α为第二象限角,cosα=-根号15/4
sin2α+cos2α=2sinacosa+2cos^2a-1=(7-根号15)/8