Question 1023431
You meant:  How to prove the identity, right?

We prove it this way.

Start with the identity {{{sec^2(x) = 1+tan^2(x)}}}

==> {{{sec^2(x) - sin^2(x) = -sin^2(x)  + sin^2(x) + cos^2(x) +tan^2(x)}}}

==>  {{{sec^2(x) - sin^2(x) = cos^2(x) +tan^2(x)}}}, and the original identity is proved...