Prove that
$csc 2 x + cot 2 x = cot x$

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Solution

$L H S = \frac{1}{sin 2 x} + \frac{cos 2 x}{sin 2 x} = \frac{2 {cos}^{2} x}{2 sin x cos x} = cot x = R H S$

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Similar questions

cot x . cot 2 x - cot 2 x . cot 3 x - cot x . cot 3 x = 1

prove that

cotx.cot2x-cot2x.cot3x-cot3x.cotx=1

{sec}^{2} x + {csc}^{2} x = {sec}^{2} x . {csc}^{2} x

\frac{1 + sin 2 x + cos 2 x}{1 + sin 2 x - cos 2 x} = cot x

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