Verify that the eqn is an identity show steps please sec4 xs

Verify that the eqn is an identity. show steps please.

sec4 xsec2 x=tan4 x+tan2 x

LHS sec^4x -sec^2x

use the identity : 1+tan^2x = sec^2x

So, (sec^2x)^2 - sec^2x

=(1 +tan^2x)^2 -( 1+tan^2x)

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

=(1 +tan^2x)(tan^2x

= tan^4x +tan^2x

= RHS

Hence it is an identity