Since sec^2θ - 1 = tan^2θ

Question

I know this is trivial, but I want to make sure I'm doing this right before I apply it to the integral I'm trying to solve...

If I have some constant a,

(a^2secθ)^2 - (a^2)^2

If I wanted to change this to tan would it be:

a^4tan^4θ?

Any help is greatly appreciated!

Answer 1

not at all.

(a^2secθ)^2 - (a^2)^2
= a^4 (sec^4θ - 1)
= a^4 (sec^2θ-1)(sec^2θ+1)
= a^4 tan^2θ (sec^2θ+1)

Answer 2

Nope. my bad. Still you were also wrong

(a^2secθ)^2 - (a^2)^2
= a^4 (sec^2θ-1)
= a^4 tan^2θ

Answer 3

So tan^2θ is where I messed up, thanks Steve!