因为cos(a-派/4)=1/4则cosacos(π/4)+sinasin(π/4)=1/4cosa+sina=4分之根号2两边平方的（sina)^2+(cosa)^2+2sinacosa=1/8而（sina)^2+(cosa)^2=1则2sinacosa=-7/8即sin2a=-7/8
