Question

-tan^2 x + sec^2 x = 1

Answer 1

to prove this you just need to rearrange the standard identity
sec^2x = 1 + tan^2 x

subtract tan^2 x from both sides:

-tan^2 x + sec^2 x = 1 + tan^2 x - tan^2 x
-tan^2 x + sec^2 x = 1

Answer 2

OK :) got it

Answer 3

if you want another way to do this:

-tan^2 x + sec^2 x

= - sin^2 x + 1
------- ------
cos^2 x cos^2 x

= 1 - sin^2 x
-----------
cos^2 x

= cos^2 x
------- = 1 (because sin^2 x + cos^2 x = 1)
cos^2 x

Answer 4

Wow thank you, yea I like this one better :)