The relation `(2*tan x)/(1 + tan^2 x) = sin 2x` has to be verified.

`(2*tan x)/(1 + tan^2 x)`

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

=> `((2*sin x)/cos x)/((cos^2x + sin^2x)/(cos^2x))`

=> `(2*sin x*cos^2 x)/(cos x*(cos^2x + sin^2x))`

=> `2*sin x*cos x`

=> `sin 2x`

**This proves that **`(2*tan x)/(1 + tan^2 x) = sin 2x`