Question

sin^2a/tg^2a + cos^2a/ctg^2a- 1/sin^2a=-ctg^2a​

Answer 1

$frac{Sin^{2}alpha}{tg^{2}alpha}+frac{Cos^{2}alpha}{Ctg^{2}alpha}-frac{1}{Sin^{2}alpha}=frac{Sin^{2}alpha Cos^{2}alpha}{Sin^{2}alpha}+frac{Cos^{2}alpha Sin^{2}alpha}{Cos^{2}alpha}-frac{1}{Sin^{2}alpha} =Cos^{2}alpha+Sin^{2}alpha-frac{1}{Sin^{2}alpha}=1-frac{1}{Sin^{2}alpha} =frac{Sin^{2}alpha-1}{Sin^{2}alpha}=frac{-Cos^{2}alpha}{Sin^{2}alpha}=-Ctg^{2} alpha\\-Ctg^{2}alpha=-Ctg^{2}alpha$

Тождество доказано