Prove :
$c o s^{2} A (1 + t a n^{2} A) = 1$

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Solution

LHS :
$c o s^{2} A (1 + t a n^{2} A)$
$= c o s^{2} A . s e c^{2} A$
$= 1$ = RHS

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Prove that:
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\frac{1 + sin 2 A + cos 2 A}{1 + sin 2 A - cos 2 A} = cot A

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