Помогите!!!Нужно упростить выражение. Created by malinka1704. algebra-ru

Помогите!!!Нужно упростить выражение...

malinka1704 @malinka1704

July 2022 1 5 Report

Помогите!!!Нужно упростить выражение

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Freakazoid

Verified answer

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

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Verified answer

2 + x) - 1 = 0...

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