Show that tan4 θ + tan2 θ = sec4 θ – sec2 θ.

LHS = tan4 θ + tan2 θ = tan2 θ (tan2 θ+1)

= tan2 θ.sec2 θ                                                                                 [∴ sec2θ = tan2 θ+1]

= (sec2 θ-1) . sec2 θ                                                                         [∴tan2θ = sec2 θ – 1]

= sec4 θ – sec2 θ = RHS