Доказать тождество! Срочно.. Created by anastasiarifma. algebra-ru

Доказать тождество! Срочно...

anastasiarifma @anastasiarifma

July 2021 1 46 Report

Доказать тождество! Срочно.

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nafanya2014

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

$\frac{1+cos \frac{ \alpha }{2}-sin \frac{ \alpha }{2} }{1-cos \frac{ \alpha }{2} -sin \frac{ \alpha }{2} } = \\ \\ =\frac{2cos ^{2}( \frac{ \alpha }{4})-2sin \frac{ \alpha }{4} cos \frac{ \alpha }{4} }{2sin ^{2}( \frac{ \alpha }{4})-2sin \frac{ \alpha }{4} cos \frac{ \alpha }{4} } = \\ \\ =\frac{2cos ( \frac{ \alpha }{4})(cos \frac{ \alpha }{4} -sin \frac{ \alpha }{4}) }{2sin( \frac{ \alpha }{4})(sin \frac{ \alpha }{4}- cos \frac{ \alpha }{4} )} =ctg \frac{ \alpha }{4}$

2 votes Thanks 1

nafanya2014 да, Вы правы

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