(cosα/2+sinα/2)^2=1+2*cosa/2*sina/2=1+sina=5/4;
sina=1/4;
cosa=负根号15/4；
cosa=cos^2a/2-sin^2a/2=(cosα/2+sinα/2)*(cosα/2-sinα/2);
所以cosα/2-sinα/2=负根号3/2;
sin2α-cos2α=2*sina*cosa-(1-2cos^2a)=-根号15/8-7/8