Prove the following identities: cosec4 A – cosec2 A = cot4 A + cot2 A - Mathematics

Prove the following identities:

cosec⁴A – cosec² A = cot⁴ A + cot² A

Sum

L.H.S. = cosec⁴A – cosec² A

= cosec² A (cosec²A – 1)

R.H.S. = cot⁴ A + cot² A

= cot² A (cot² A + 1)

= (cosec² A – 1) cosec² A

Thus, L.H.S. = R.H.S.

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