sec^4 + sec^2tan^2x - 2tan^4x=?

Answer 1

sec^4 x + sec^2x tan^2x - 2tan^4x = sec^2x (sec^2 x + tan^2 x) - 2tan^4 x = (1 + tan^2 x) (1 + 2 tan^2 x) - 2 tan^4 x =
1 + 3 tan^2 x + tan^4 x - 2tan^4 x = 1 + 3 tan^2 x - tan^4 x

I don't see how to get to something nicer.

Answer 2

my calculator gives me x=46.19 when i set that equation equal to 0 and solve for x...
let me make sure i typed it in right...
(1/cosx)^4 + (1/cosx)^2 * (tanx)^2 * x - 2(tanx)^4 * x = 0
x=46.19