Question

Доказать тождество.
$\frac{sin4a+sin9a-sina}{cos4a+cosa+cos9a}=tg4a$

Answer 1

$\frac{sin4 \alpha +sin9 \alpha -sin \alpha }{cos4 \alpha +cos \alpha +cos9 \alpha } = \frac{sin4 \alpha +2sin4 \alpha cos5 \alpha }{cos4 \alpha +2cos5 \alpha cos4 \alpha } = \frac{sin4 \alpha (1+2cos5 \alpha )}{cos4 \alpha (1+2cos5 \alpha )} = \frac{sin4 \alpha }{cos4 \alpha } =tg4 \alpha$