is the azimuthal equidistant projection of the globe angle preserving

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is the azimuthal equidistant projection of a sphere, the inverse of which takes the general point (x,y) to the point $$\bigg(\cos\left(\sqrt{x^2+y^2}\right)\cdot\frac{x}{\sqrt{x^2+y^2}},\cos\left(\sqrt{x^2+y^2}\right)\cdot\frac{y}{\sqrt{x^2+y^2}},\sin\left(\sqrt{x^2+y^2}\right)\bigg)$$ angle preserving?