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

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Prove the following trigonometric identities:

sec4A(1-sin4A)-2tan2A=1

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sec4A(1 - sin4A) - 2tan2A

= sec4A - sec4sin4A -2tan2A

= sec4A - \(\frac{sin^4A}{cos^4A}\) - 2tan2A

= (sec2A)2 - tan4A - 2tan2A

= (1+tan2A)2 - tan4A - 2tan2A

= 1+tan4A + 2tan2A - tan4A - 2tan2A

= 1

Hence Proved.

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