[Risolto] N135 non riesco a capire come si debbano fare questi esercizi di semplificazione

$sin^2 \alpha -tan^2 \alpha=$

$=sin^2 \alpha -\frac{sin^2 \alpha}{cos^2 \alpha}=$

$=sin^2 \alpha -\frac{sin^2 \alpha}{1-sin^2 \alpha}=$

$=\frac{sin^2 \alpha(1-sin^2 \alpha)-sin^2 \alpha}{1-sin^2 \alpha}=$

$=\frac{sin^2 \alpha-sin^4 \alpha-sin^2 \alpha}{1-sin^2 \alpha}=$

$=\frac{-sin^4 \alpha}{1-sin^2 \alpha}=$

$=\frac{sin^4 \alpha}{sin^2 \alpha -1}$