Prove the following identities : cosec^4 A - cosec^2 A = cot^4 A + cot^2 A

Solving L.H.S. of the equation : ⇒ cosec 4 A - cosec 2 A ⇒ cosec 2 A(cosec 2 A - 1) By formula, cosec 2 A = 1 + cot 2 A ⇒ (1 + cot 2 A)(1 + cot 2 A - 1) ⇒ (1 + cot 2 A)cot 2 A ⇒ cot 2 A + cot 4 A. Since, L.H.S. = R.H.S. Hence, proved that cosec 4 A - cosec 2 A = cot 4 A + cot 2 A.

Mathematics

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

Trigonometric Identities

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Answer

Solving L.H.S. of the equation :

⇒ cosec⁴ A - cosec² A

⇒ cosec² A(cosec² A - 1)

By formula,

cosec² A = 1 + cot² A

⇒ (1 + cot² A)(1 + cot² A - 1)

⇒ (1 + cot² A)cot² A

⇒ cot² A + cot⁴ A.

Since, L.H.S. = R.H.S.

Hence, proved that cosec⁴ A - cosec² A = cot⁴ A + cot² A.

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

Trigonometric Identities

Answer

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

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