Помогите!!!Нужно упростить выражение

Решите задачу:

$cos^2(a-\frac{\pi}{4})-cos^2(a+\frac{\pi}{4})=\\(cos(a-\frac{\pi}{4})-cos(a+\frac{\pi}{4}))(cos(a-\frac{\pi}{4})+cos(a+\frac{\pi}{4}))=\\(-2sin\frac{a-\frac{\pi}{4}+a+\frac{\pi}{4}}{2}sin\frac{a-\frac{\pi}{4}-a-\frac{\pi}{4}}{2})(2cos\frac{a-\frac{\pi}{4}+a+\frac{\pi}{4}}{2}cos\frac{a-\frac{\pi}{4}-a-\frac{\pi}{4}}{2})=\\(-2sinasin(-\frac{\pi}{4}))(2cosacos(-\frac{\pi}{4}))=\\(2*\frac{\sqrt2}{2}*sina)(2*\frac{\sqrt2}{2}*cosa)=(\sqrt2sina)(\sqrt2cosa)=\\2sinacosa=sin2a.$