Question

prove that {1+1/tan2A} * {1+1/cot2A} = 1/(sin2A-sin4A)

Answer 1

$left \: side = (1 + \frac{1}{ { \tan(a) }^{2} } )(1 + \frac{1}{ { \cot(a) }^{2} } ) \\ = (1 + { \cot(a) }^{2} )(1 + { \tan(a) }^{2} ) \\ = { \csc(a) }^{2} \times { \sec(a) }^{2} \\ = \frac{1}{ { \sin(a) }^{2} } \times \frac{1}{ { \cos(a) }^{2} } \\ = \frac{1}{ { \sin(a) }^{2} { \cos(a) }^{2} } \\ = \frac{1}{ { \sin(a) }^{2} (1 - { \sin(a) }^{2}) } \\ = \frac{1}{ { \sin(a) }^{2} - { \sin(a) }^{4} } \\ = right \: side \\ hence \: proved$

Answer 2

Answer:

Answers is given hope it will help you