Prove the following identity:
$(1 - s i n^{2} A) s e c^{2} A = 1$

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Solution

We have,
$L H S = (1 - s i n^{2} A) s e c^{2} A$
$= c o s^{2} A s e c^{2} A$
$= c o s^{2} A (\frac{1}{c o s^{2} A})$
$= 1 = R H S$

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