Question

Cosec⁴Q-Cosec²Q=Cot⁴Q+Cot²Q Solve it​

Answer 1

Step-by-step explanation:

Q: cosec⁴A - cosec²A = cot⁴A + cot²A

As we know, cosec²A - cot²A = 1

→ cosec²A = 1 + cot²A

So, On solving LHS of the question, we get:

cosec⁴A - cosec²A

= (cosec²A)² - cosec²A

= (1 + cot²A)² - (1 + cot²A)

= ( 1 + (cot²A)² + 2 cot²A ) - 1 - cot²A

= 1 + cot⁴A + 2 cot²A - 1 - cot²A

= cot⁴A + cot²A

So, LHS = RHS

Hence, Proved.

Thanks!