упростите cos^4a-sin^4a/cos2a. Created by Nishinoyaa. algebra-ru

cos2a...

Nishinoyaa @Nishinoyaa

July 2022 1 7 Report

упростите cos^4a-sin^4a/cos2a

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snow99

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В числителе видим формулу разности квадратов:
$\frac{ {cos}^{4} \alpha - {sin}^{4} \alpha }{cos2 \alpha } = \frac{( {cos}^{2} \alpha - {sin}^{2} \alpha )( {cos}^{2} \alpha + {sin}^{2} \alpha )}{cos2 \alpha }$
В знаменателе используем формулу косинуса двойного угла:
$= \frac{( {cos}^{2} \alpha - {sin}^{2} \alpha )( {cos}^{2} \alpha + {sin}^{2} \alpha ) }{ {cos}^{2} \alpha - {sin}^{2} \alpha } = {cos}^{2} \alpha + {sin}^{2} \alpha$
Получили основное тригонометрическое тождество:
${cos}^{2} \alpha + {sin}^{2} \alpha = 1$
Ответ: 1.

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