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Simplify: ( 1 + tan^2 A)/( 1+ cot^2 A)

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$\frac{1+\tan ^{2}A}{1+\cot ^{2}A}\\\\= \frac{1+\tan ^{2}A}{1+\frac{1}{\tan ^{2}}A}\\ = \tan^2A\times(\frac{1+\tan^2 A}{1+\tan^2A})\\ = \tan^2A$

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Ravindra Pindel

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