Prove the following identities : sec 4 A (1 - sin 4 A) - 2 tan 2 A = 1

Solving L.H.S. of the above equation : ⇒ sec 4 A (1 - sin 4 A) - 2 tan 2 A ⇒ sec 4 A (1 - sin 2 A)(1 + sin 2 A) - 2 tan 2 A By formula, 1 - sin 2 A = cos 2 A ⇒ sec 4 A cos 2 A (1 + sin 2 A) - 2 tan 2 A ⇒ sec 4 A (1 + sin 2 A) - 2 tan 2 A ⇒ sec 2 A (1 + sin 2 A) - 2 tan 2 A ⇒ sec 2 A + sec 2 A sin 2 A - 2 tan 2 A ⇒ sec 2 A + sin 2 A - 2 tan 2 A ⇒ sec 2 A + tan 2 A - 2 tan 2 A ⇒ sec 2 A - tan 2 A ⇒ 1. Since, L.H.S. = R.H.S. Hence, proved that sec 4 A (1 - sin 4 A) - 2 tan 2 A = 1.

Mathematics

Prove the following identities :
sec⁴ A (1 - sin⁴ A) - 2 tan² A = 1

Trigonometric Identities

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Mathematics

Prove the following identities :
sec⁴ A (1 - sin⁴ A) - 2 tan² A = 1

Trigonometric Identities

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Mathematics

Prove the following identities :sec4 A (1 - sin4 A) - 2 tan2 A = 1

Trigonometric Identities

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Prove the following identities :(1 + tan A + sec A)(1 + cot A - cosec A) = 2

Prove the following identities :
sec⁴ A (1 - sin⁴ A) - 2 tan² A = 1

Prove the following identities :
(1 + tan A + sec A)(1 + cot A - cosec A) = 2