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)##

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