Solving from one side sec4x - sec2x = tan4x + tan2x
sec^4 x - sec^2x =
factor out sec^2 x
sec^2 x ( sec ^2 x - 1) =
{ tan^2 x + 1 = sec^2 x }
(tan^2 x + 1) (tan^2 x) =
tan^4 x + tan^2 x