sec4 A − sec2 A is equal to

The given expression is $\sec ^{4} \mathrm{~A}-\sec ^{2} \mathrm{~A}$.

Taking common $\sec ^{2} \mathrm{~A}$ from both the terms, we have

$\sec ^{4} A-\sec ^{2} A$

$=\sec ^{2} \mathrm{~A}\left(\sec ^{2} \mathrm{~A}-1\right)$

$=\left(1+\tan ^{2} \mathrm{~A}\right) \tan ^{2} \mathrm{~A}$

$=\tan ^{2} \mathrm{~A}+\tan ^{4} \mathrm{~A}$

Disclaimer: The options given in (c) and (d) are same by the commutative property of addition.

Therefore, the correct options are (c) or (d).