sec⁴ A − sec² A is equal to

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