Question

Докажите тождество: $frac{cos ^{2} alpha - sin^{2} alpha }{ctg alpha -tg alpha } =sin alpha *cos alpha$

Answer 1

$frac{cos^2 alpha -sin^2 alpha }{ctg alpha -tg alpha } = frac{cos^2 alpha -sin^2 alpha }{ frac{cos alpha }{sin alpha }- frac{sin alpha }{cos alpha } } =frac{sin alpha cos alpha (cos^2 alpha -sin^2 alpha )}{cos^2 alpha -sin^2 alpha } =sin alpha cos alpha$