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

Question

Prove identity


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

Answer 1

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)`