Докажите тождество 1-tg@/1+tg@ = 1 - sin2@/cos2@ @-альфа. Created by OpenOffice. algebra-ru

cos2@ @-альфа...

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July 2022 1 11 Report

Докажите тождество
1-tg@/1+tg@ = 1 - sin2@/cos2@
@-альфа

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Freakazoid

Verified answer

Преобразуем правую часть равенства.
$\frac{1-tga}{1+tga}=\frac{1-sin2a}{cos2a}\\\frac{cos^2a-2sinacosa+sin^2a}{cos^2a-sin^2a}=\frac{(cosa-sina)^2}{(ccosa-sina)(cosa+sina)}=\frac{cosa-sina}{cosa+sina}=\\ \frac{\frac{cosa}{cosa}-\frac{sina}{cosa}}{\frac{cosa}{cosa}+\frac{sina}{cosa}}=\frac{1-tga}{1+tga}$

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