Question

prove the above trigonometric relation .​

Answer 1

Answer:

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Refer to attachment for 100% wrong answer.

Answer 2

Answer:

LHS :$(sin^{4} \theta- cos^{4}\theta + 1 ) cosec^{2} \theta$

⇒$( ( sin^{2}\theta)^{2} - ( cos^{2}\theta)^{2} + 1) cosec^{2} \theta$

⇒$( (sin^{2} \theta - cos^{2} \theta) ( sin^{2} \theta + cos^{2} \theta) +1 ) cosec^{2} \theta$

⇒$( ( sin^{2} \theta - cos^{2} \theta) (1) + 1) cosec^{2} \theta$

⇒$[((sin^{2} \theta - (1- sin^{2} \theta)) +1] cosec^{2} \theta$

⇒$(sin^{2} \theta - 1 + sin^{2} \theta +1) cosec^{2} \theta$

⇒$(2sin^{2} \theta)cosec^{2} \theta$

⇒$(\frac{2sin^{2}\theta }{1} ) ( \frac{1}{sin^{2} \theta} )$

⇒2 = R.H.S