Question

Verifique as identidades:


tgx-cotgx/tg+cotgx=2sen^2-1

Answer 1

$\frac{tgx-cotgx}{tgx+cotgx} = \frac{ \frac{senx}{cosx}- \frac{cosx}{senx}}{ \frac{senx}{cosx}+ \frac{cosx}{senx}} = \frac{ \frac{ sen^{2}x- cos^{2}x }{senx.cosx} }{ \frac{ sen^{2}x+ cos^{2}x }{senx.cosx} } =sen^{2}x-cos^{2}x$

$sen^{2}x-cos^{2}x=sen^{2}x -(1-sen^{2}x )=2sen^{2}x-1$