Question

Prove the following identities:
() cosec2A +cot 2 A=cot A​

Answer 1

Answer:

$L. H. S \\ =cosec \: 2A + cot \: 2A \\ = \frac{1}{sin \: 2A} + \frac{cos \: 2A }{sin \: 2A} \\ = \frac{1 + cos \: 2A }{sin \: 2A} \\ = \frac{1 + 2 {cos}^{2} \: A - 1}{2 \: sin \:A.cos \: A} \\ = \frac{ 2 {cos}^{2} \: A }{2 \: sin \:A.cos \: A} \\ = \frac{ cos \: A }{ \: sin \:A} \\ = cot \: A \\ = </p><p>R. H. S. \: \\ hence \: proved$