Question
Prove that:
$\left(\frac{1+\tan ^2 A}{1+\cot ^2 A}\right)=\frac{(1-\tan A)^2}{(1-\cot A)^2}$

Answer

$ \text { LHS } =\frac{1+\tan ^2 A}{1+\frac{1}{\tan ^2 A}}$
$ =\tan ^2 A$
$ \text { RHS } =\frac{(1-\tan A)^2}{\left(1-\frac{1}{\tan A}\right)^2}$
$ =\tan ^2 A$
$\therefore \text { LHS }=\text { RHS }$

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