Prove the Identity : \( \sec^4 x – \sec^2 x = \tan^4 x + \tan^2 x \)

Solution:

\[ \sec^4 x – \sec^2 x \]

\[ = \sec^2 x(\sec^2 x-1) \]

\[ = \sec^2 x \tan^2 x \]

\[ = (1+\tan^2 x)\tan^2 x \]

\[ = \tan^2 x+\tan^4 x \]

\[ = \tan^4 x+\tan^2 x \]

Hence proved.