Question

Verificati egalitatea: (1-tg^2x)/(1+tg^2x)=cos2x

Answer 1

$\frac{1- tg^{2}x }{1+ tg^{2}x }= \frac{1- \frac{ sin^{2}x }{ cos^{2}x } }{1+ \frac{ sin^{2} x}{ cos^{2}x } }$
Aducem la acelasi numitor:$\frac{ cos^{2}x- sin^{2}x }{ sin^{2}x+ cos^{2}x } = \frac{ cos^{2}x-sin^{2}x}{1} =cos2x$