Question

cosec^4A+cosec^2A=cot^4A+cot^2A​

Answer 1

QUESTION:

Prove that

cosec⁴A - cosec²A = cot⁴A +cot²A

USED FORMULAS:

cosec²A - cot²A = 1

cot²A = cosec²A - 1

cosec²A = 1 + cot²A

ANSWER:

Taking LHS

cosec⁴A + cosec²A

Taking common cosec²A

= cosec²A(cosec²A - 1)

= cosec²A(cot²A)

= (1 + cot²A)(cot²A)

= cot²A + cot⁴A

LHS = RHS

Hence proved

CONCEPT'S USED:

⟩⟩ trigonometric identities

⟩⟩ trigonometric ratios

NOTE:

In your question one mistake is there in LHS cosec⁴A + cosec²A not + between them it's ' - ' ( minus) check it