What is 1-tan^2x?

Question

Why can't we say that as 1+sec^2x=tan^2x that 1-tan^2x=-sec^2x?

Edit: Here I made a mistake

It is 1+tan^2x = sec^2x

So there isn't a really simple way to get 1-tan^2x.



Answer 1

1 + tan²x = sec²x

So, tan²x = sec²x - 1

Thus, 1 - tan²x = 1 - (sec²x - 1) = 2 - sec²x

Answer 2

Well, if we add tan^2x + sec^2x to both sides of your 2nd equation, you get the first equation. So you can say it, and you will be correct. :-)