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Prove the following identity, where the...

Prove the following identity, where the angles involved are acute angles for which the expressions are defined.
(x) `((1+tan^2A)/(1+cot^2A))=((1-tanA)/(1-cotA))^2=tan^2A`

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To prove the identity \[ \frac{1 + \tan^2 A}{1 + \cot^2 A} = \left(\frac{1 - \tan A}{1 - \cot A}\right)^2 = \tan^2 A, \] we will break it down into manageable parts. ...
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