Доказать тождество.......... . Created by dilay051005. algebra-ru

Объяснение:Упростим числитель:Упростим знаменатель:

Доказать тождество.......... ...

dilay051005 @dilay051005

September 2021 1 8 Report

Доказать тождество..........

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sangers1959

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Объяснение:

Упростим числитель:

$sin5\beta +sin\beta =2*sin\frac{5\beta +\beta }{2}*cos\frac{5\beta -\beta }{2}=2*sin3\beta *cos2\beta .\ \ \ \ \Rightarrow\\sin3\beta +2*sin3\beta *cos2\beta =sin3\beta *(1+2*cos2\beta ).$

Упростим знаменатель:

$cos5\beta +cos\beta =2*cos\frac{5\beta +\beta }{2}*cos\frac{5\beta -\beta }{2}=2*cos3\alpha *cos2\alpha \ \ \ \ \Rightarrow\\cos\beta +cos5\beta +cos3\beta =cos3\beta +2*cos3\beta *cos2\beta =cos3\beta (1+2*cos2\beta ).$

$\frac{sin3\beta *(1+2cos2\beta )}{cos3\beta *(1+2cos2\beta )} =\frac{sin3\beta }{cos3\beta } =tg3\beta .$

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