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`
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