sec^4x+sec^2x•tan^2x-2tan^4x=?

Question

Complete the identity.

Answer 1

sec^4x + sec^2x • tan^2x - 2tan^4x

Start by factoring, maybe??

The factors: (omitting the "x" for clarity)

(sec^2 + tan^2) * (sec^2 - 2tan^2)

Then, I think this identity will be useful:

1 + tan^2 = sec^2

EDIT: Let's try it:

replace sec^2 with 1+tan^2:

(1 + tan^2 + tan^2) * (1 + tan^2 - 2tan^2)

(1 + 2tan^2 ) * (1 - tan^2)

1 + tan^2 - 2tan^4

Somebody check and see if I did this right....

Answer 2

sec=1/cos

Without a value for "x"; I don't know what to tell you.