Question

Докажите тождество
$1+tg^2a= frac{tg^2a}{sin^2a}$

Answer 1

$1+tg^2alpha= displaystyle 1+frac{sin^2alpha}{cos^2alpha} = frac{cos^2alpha+sin^2alpha}{cos^2alpha}= frac{1}{cos^2alpha} = frac{sin^2alpha}{cos^2alphasin^2alpha} = frac{tg^2alpha}{sin^2alpha}$