# sec4 A − sec2 A is equal toA. tan2 A − tan4 AB. tan4 A − tan2 AC. tan4 A + tan2 AD. tan2 A + tan4 A

Note: Since all the options involve the trigonometric ratio tan θ, so we use the identity 1 + tan2 θ = sec2 θ.

To find: sec4 A – sec2 A

Consider sec4 A – sec2 A = (sec2 A)2 – sec2 A

Now, as sec2 A = 1 + tan2 A

sec4 A – sec2 A = (sec2 A)2 – sec2 A

= (1 + tan2 A)2 – (1 + tan2 A)

= 1 + tan4 A + 2 tan2 A – 1 – tan2 A

= tan4 A + tan2 A

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