Question

please slove this question ​

Answer 1

Refer to the attachment.

Answer 2

Step-by-step explanation:

We Have :-

$( \sin^{4} (\theta) - \cos^{4} (\theta) + 1) \csc^{2} (\theta)$

To Prove :-

$( \sin^{4} (\theta) - \cos^{4} (\theta) + 1) \csc^{2} (\theta) = 2$

Solution :-

$( \sin^{4} (\theta) - \cos^{4} (\theta) + 1) \csc^{2} (\theta) \\ \\ \\ ((( \sin ^{2} (\theta) + \cos^{2} (\theta) )(\sin ^{2} (\theta) - \cos^{2} (\theta) ) + 1) \csc^{2} (\theta) \\ \\ \\ ((\sin ^{2} (\theta) - \cos^{2} (\theta) ) + 1) \csc^{2} (\theta) \\ \\ \\ (\sin ^{2} (\theta) + (1 - \cos^{2} (\theta) ) ) \csc^{2} (\theta) \\ \\ \\ (\sin ^{2} (\theta) +\sin ^{2} (\theta)) \csc^{2} (\theta) \\ \\ \\ 2\sin ^{2} (\theta)\csc^{2} (\theta) \\ \\ \\ 2 \\ \\ \\ = rhs \\ \\ \\ hence \: proved$