Deriving the atan2 Function from Tangent Half-Angle Formulas

[mnb96]

Hello, it is mentioned http://en.wikipedia.org/wiki/Atan2#Definition" that using the tangent half-angle formulas it is possible to express the function atan2 as:

\mathrm{atan2}(y,x)=2\mathrm{arctan}\frac{y}{\sqrt{x^2+y^2}+x}

How can I derive this result?

 

[tiny-tim]

Put y = rsinθ, x = rcosθ, then y/(√(x² + y²) + x) = sinθ/(1 + cosθ),

which you should be able to prove is tan(θ/2)

 

[mnb96]

Thanks!
Now it´s clear where that formula came from.