Not at all.
Take
(1-tan^2x)/(1+tan^2x)
Multiply and divide by cos^2x. You get
[cos^2x - tan^2x*cos^2x]/[cos^2x + tan^2x*cos^2x]
I hope, you know that tanx = sinx/cosx and basic indentity cos^2x + sin^2x = 1
So you get
[cos^2x - sin^2x]/[cos^2x + sin^2x]
= [cos^2x - sin^2x] = cos(2x)