Question

Prove identity
$\frac{1 - \tan {}^{2} (x) }{ \cot {}^{2} (x) - 1 } = \tan {}^{2} (x)$
Prove identity​

Answer 1

Step-by-step explanation:

$\frac{1 - \tan {}^{2} (x) }{ \cot {}^{2} (x) - 1} = \tan {}^{2} (x)$

$\frac{1 - \frac{ \sin {}^{2} (x) }{ \cos {}^{2} (x) } }{ \frac{ \cos {}^{2} (x) }{ \sin {}^{2} (x) } - 1 }$

$\frac{ \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{ \cos {}^{2} (x) } }{ \frac{ \cos {}^{2} (x ) - \sin {}^{2} (x) }{ \sin {}^{2} (x) } }$

$\frac{ \sin {}^{2} (x) }{ \cos {}^{2} (x) } = \tan {}^{2} (x)$

$\tan {}^{2} (x) = \tan {}^{2} (x)$