Question

Доказать тождество sin2a-tga=cos2atga

Answer 1

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