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Trigonometric Identities

Prove the fol...

Question

Prove the following trignometric identities:

$c o s^{2} A + \frac{1}{1 + c o t^{2} A} = 1$

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Solution

We know that,

$c o s^{2} θ + s i n^{2} θ = 1$

$c o s e c^{2} θ - c o t^{2} θ = 1$

So, $c o s^{2} A + \frac{1}{1 + c o t^{2} A} = c o s^{2} A + \frac{1}{c o s e c^{2} A}$

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

= 1

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