Question

prove the identity

Answer 1

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

Answer 2

Factor the left side. It is the difference of two squares.

Answer 3

completing what @Mertsj is trying to say, the LHD becomes
\[(\sec^2(x)+\tan^2(x))(\tan^2(x)+1-tant^2(x))\]=RHS

Answer 4

Ah, ok. Thank you :)

Answer 5

you are welcome :)