найдите tg a,если sin a=2корня из 29/29 и а принадлежит (о,п/2). Created by akoryagina. algebra-ru

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akoryagina @akoryagina

July 2022 1 10 Report

найдите tg a,если sin a=2корня из 29/29 и а принадлежит (о,п/2)

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$\tan \alpha= \frac{\sin \alpha}{\cos \alpha}$
$\cos \alpha= \sqrt{1-\sin^2\alpha}= \sqrt{1- \frac{29}{841} } = \sqrt{ \frac{812}{841} } = \frac{2 \sqrt{203} }{29}$
$\tan \alpha= \frac{29\sqrt{29}}{29*2 \sqrt{203}}= \sqrt{ \frac{29}{812} }= \sqrt{ \frac{1}{28} } = \frac{ \sqrt{28} }{28}= \frac{\sqrt{7} }{14}$

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