Question

Prove that
Cosec 2A - cot 2A = tan A ?​

Answer 1

Answer:

$\huge\bf\underline\green{AnSweR:}$

Cosec 2A - Cot 2A = tan A

$\csc2a \: - \cot2a = \frac{1}{ \sin \: 2a} - \frac{ \cos \: 2a }{ \sin \: 2a}$

$= \frac{1 - \cos \: 2a}{ \sin \: 2a }$

$= \frac{2 \: { \sin}^{2}a }{2 \: \sin \: a \: cos \: a }$

$= \frac{ \sin \: a}{ \cos \: a }$

$\implies\bf\red{tan\:A}$

$\bf\blue{Hence\:Proved}$

Answer 2

Step-by-step explanation:

$\csc(2a) - \cot(2a) = \frac{1}{ \sin(2a) } - \frac{ \cos(2a) }{ \sin(2a) }$

$= \frac{1 - \cos(2a) }{ \sin(2a) }$

$= \frac{2 \sin ^{2} (a) }{(2 \sin(a) \cos(a) ) }$

$= \frac{ \sin(a) }{ \cos(a) }$

$= \tan(a)$