Question

Помогите!!!Нужно упростить выражение

Answer 1

$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}))=\(-2sinfrac{a-frac{pi}{4}+a+frac{pi}{4}}{2}sinfrac{a-frac{pi}{4}-a-frac{pi}{4}}{2})(2cosfrac{a-frac{pi}{4}+a+frac{pi}{4}}{2}cosfrac{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.$