Question

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

Answer 1

Call `tan (x/2) = t` and use the trig identity

`cos x = (1 - t^2)/(1 + t^2)`, then

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