Упростить [tex]tg \alpha (1+cos2 \alpha ) [/tex]. Created by Nikita1klon. matematika-ru

tex]...

Luluput

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$tg \alpha (1+cos2 \alpha )=tg \alpha *2cos^2
\alpha = \frac{sin \alpha }{cos \alpha } *2cos^2 \alpha =2cos \alpha sin \alpha
=sin2 \alpha$

Воспользовались следующими формулами:

$\frac{1+cosx}{2}=cos^2 \frac{x}{2}$
$sin2x=2sinxcosx$

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iosiffinikov

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Cos2a=cos^2(a)-sin^2(a)=-1+2cos^2(a)
2cos^2(a)=1+cos2a
tga*(1+cos2a)=2sina*cosa=sin2a
Ответ: sin2a

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