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

asked Jan 22, 2023 151k views

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Prove identity

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

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Explanation:

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

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

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

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

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

Starwave answered Jan 27, 2023

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