Question

Докажите тождество
$sin2a-tga=cos2a*tga$

Answer 1

$sin2 \alpha -tg \alpha = \\ =2sin \alpha cos \alpha - \dfrac{sin \alpha }{cos \alpha } = \\ = \dfrac{2sin \alpha cos^2 \alpha -sin \alpha }{cos \alpha } = \\ = \dfrac{sin \alpha (2cos^2 \alpha -1)}{cos \alpha } = \\ =cos2 \alpha tg \alpha$