Use Trig identities to verify that sec^4(x)-tan^4(x)=1+2tan^2(x), Only work with one side of the equation

Answer 1

sec^4(x) - tan^4(x) =
= (1 + tan^2(x))^2 - tan^4(x)
= 1 + 2tan^2(x) + tan^4(x) - tan^4(x)
= 1 + 2tan^2(x)

QED