Prove the following identities
sec4x – sec2x = tan4x + tan2x
LHS = sec4x – sec2x
= (sec2x) 2 – sec2x
We know sec2 θ = 1 + tan2 θ.
= (1 + tan2x) 2 – (1 + tan2x)
= 1 + 2tan2x + tan4x – 1 - tan2x
= tan4x + tan2x = RHS
Hence proved.