Question

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

Answer 1

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