Prove the following trigonometric identities:

$s i n^{2} A c o t^{2} A + c o s^{2} A t a n^{2} A = 1$

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[RD Sharma]
[Trigonometic Ratios]

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$\frac{s e c A - t a n A}{s e c A + t a n A} = \frac{c o s^{2} A}{(1 + s i n A)^{2}}$