How do you prove ##(1 + tan^2x)/(1-tan^2x) = 1/(cos^2x - sin^2x)##?

To prove ##(1+tan^x)/(1-tan^2x)=1/(cos^x -sin^2x)##

use the following identities:

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

and

##tanx = sinx/cosx##

Steps :

Step 1 : ##(1+tan^2x)/(1-tan^2x)##

Step 2 : ##(1+(sin^2x/cos^2x))/(1-(sin^2x/cos^2x))##

Step 3 : ##((cos^2+sin^2x)/cancel(cos^2x))/((cos^2x-sin^2x)/cancel(cos^2x))##

Step 4 : ##(cos^2x + sin^2x)/(cos^2x - sin^2x)##

Step 5 : ##1/(cos^2x - sin^2x)##