Prove the following trigonometric identities.

$\cos^{2} A + \frac{1}{1 + \cot^{2} A} = 1$

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Solution

We know that,

So,

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Prove the following trigonometric identities:

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

\frac{\tan^{2} A}{1 + \tan^{2} A} + \frac{\cot^{2} A}{1 + \cot^{2} A} = 1

\frac{1 + \cos A}{\sin^{2} A} = \frac{1}{1 - \cos A}

\frac{\cot^{2} A (\sec A - 1)}{1 + \sin A} = \sec^{2} A (\frac{1 - \sin A}{1 + \sec A})

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