sinα+cosα=1/2 求cos2α:
(sinα+cosα)^2=(sinα)^2+(cosα)^2+2sinαcosα=1/4
所以1+2sinαcosα=1/4
进而sin2α=2sinαcosα=-3/4
因为(sin2α)^2+(cos2α)^2=1
所以cos2α=+/-(根号7)/4