Question

Доказать тождество:
1-2sin^2a/sina cosa=ctga-tga

Answer 1

$\frac{1-2sin^{2} \alpha }{sin \alpha * cos \alpha } = \frac{cos^2 \alpha }{sin \alpha * cos \alpha} - \frac{sin^2 \alpha }{sin \alpha * cos \alpha} = \frac{cos \alpha }{sin \alpha } - \frac{sin \alpha }{cos \alpha } =ctg \alpha -tg \alpha \\ \\ 1-2sin^2 \alpha =cos2 \alpha \\ cos2 \alpha =cos^2 \alpha -sin^2 \alpha$