Упростить выражение ((sina-cosa)^2-1)/((sin^2)a-(cos^2)a-1. Created by Boris77777. matematika-ru

((sin^2)a-(cos^2)a-1...

November 2021 1 49 Report

Упростить выражение ((sina-cosa)^2-1)/((sin^2)a-(cos^2)a-1

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DimaPuchkov $\frac{(\sin \alpha - \cos \alpha)^2 -1}{\sin^2 \alpha - \cos^2 \alpha -1}=\frac{\sin^2 \alpha -2 \sin \alpha \cos \alpha +\cos^2 \alpha -1}{-1+\sin^2 \alpha - \cos^2 \alpha}=\frac{\sin^2 \alpha +\cos^2 \alpha -1 -2 \sin \alpha \cos \alpha}{-1+\sin^2 \alpha - \cos^2 \alpha}=\\ \\ = \frac{1 -1 -2 \sin \alpha \cos \alpha}{-(1-\sin^2 \alpha) - \cos^2 \alpha}=\frac{-2\sin \alpha \cos \alpha}{-\cos^2 \alpha - \cos^2 \alpha}=\frac{-2\sin \alpha \cos \alpha}{-2\cos^2 \alpha }=\frac{\sin \alpha}{\cos \alpha}=$ $=tg \, \alpha$

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