упростите выражение (1-cos^альфа)tg^2альфа+1-tg^2альфа. Created by pozhidaevad. algebra-ru

упростите выражение (1-cos^альфа)tg^2альфа+1-tg^2альфа...

pozhidaevad @pozhidaevad

July 2022 1 3 Report

упростите выражение
(1-cos^альфа)tg^2альфа+1-tg^2альфа

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ProGroomer

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$(1-cos^2\alpha)tg^2\alpha+1-tg^2\alpha=\sin^2\alpha *tg^2\alpha+1-tg^2\alpha=\\={sin^4\alpha+sin^2\alpha*cos^2\alpha+cos^4\alpha-sin^2\alpha\over cos^2\alpha}={sin^4\alpha+sin^2\alpha*(-sin^2\alpha)+cos^4\alpha\over cos^2\alpha}=cos^2\alpha$

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