Question

Доказать тождество:
ctgα/tgα+ctgα = cos²α

Answer 1

$dfrac{ctg alpha }{tg alpha +ctg alpha } = dfrac{tg alpha cdot ctg alpha }{tg alpha cdot tg alpha +tg alpha cdot ctg alpha } = dfrac{1}{tg^2 alpha +1} = dfrac{1}{ frac{1}{cos^2 alpha } } =cos^2 alpha$