How does tan^4x-sec^4x equal -2tan^2x-1

Question

If someone could please explain to me then that would be awesome. Thank you ^^

Answer 1

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

Reiny, imagine the missing x's are present!

Answer 2

Ohhh that makes a lot of sense, thank you!

Answer 3

Steve, as long as they are not imaginary.