Упростите выражение.Только б.Даю 50 баллов,только быстро.. Created by msteymomsen. algebra-ru

Упростите выражение.Только б.Даю 50 баллов,только быстро...

msteymomsen @msteymomsen

August 2022 1 5 Report

Упростите выражение.Только б.Даю 50 баллов,только быстро.

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NNNLLL54

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$1)\; \; \alpha + \beta =\pi \\\\cos(\alpha -\beta )-2sin\alpha \, sin\beta =\\\\=cos\alpha \, cos\beta +sin\alpha \, sin\beta -2sin\alpha \, sin\beta =cos\alpha \, cos\beta -sin\alpha \, sin\beta =\\\\=cos(\alpha +\beta )=cos\pi =-1\\\\2)\; \; \alpha \ne \frac{\pi n}{2}\; ,\; n\in Z\\\\cos^2\alpha -\frac{cos(\pi - \alpha )sin(\frac{\pi}{2}- \alpha )}{ctg(\pi + \alpha )tg(\frac{3\pi }{2}- \alpha )}=cos^2\alpha -\frac{-cos \alpha\cdot cos\alpha }{ctg\alpha \cdot ctg\alpha }=\\\\=cos^2\alpha -\frac{cos^2\alpha }{cos^2\alpha /sin^2\alpha }=cos^2\alpha -sin^2\alpha =cos2\alpha$

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