Question

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

Answer 1

`LHS =(1 + tan^2x)/(1-tan^2x)`

`=(1+sin^2x/cos^2x)/(1-sin^2x/cos^2x)`

`=((cos^2x+sin^2x)/cos^2x)/((cos^2x-sin^2x)/cos^2x)`

`= (sin^2x+cos^2x)/(cos^2x - sin^2x) =RHS`