Question

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

Answer 1

That's true only if `cos^2 x = 1 Rightarrow x in pi ZZ`

Explanation:

`1 + tan^2 x / (1- tan^2 x) = 1 + frac{sin^2 x/ cos^2 x}{ 1- sin^2 x/cos^2 x} =`

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

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