If we are given the transformation:
$$X=\ln (1+\sqrt x\cos y)$$ $$Y=2\sqrt x (1+\sqrt x\cos y)\sin y$$
Would the inverse transformation be:
$$x={Y^2\over 4\exp (2X)}+(\exp (X)-1)^2$$
$$y=\arctan \left({Y\over 2\exp(X)(\exp(X)-1)}\right)$$ ?
If we are given the transformation:
$$X=\ln (1+\sqrt x\cos y)$$ $$Y=2\sqrt x (1+\sqrt x\cos y)\sin y$$
Would the inverse transformation be:
$$x={Y^2\over 4\exp (2X)}+(\exp (X)-1)^2$$
$$y=\arctan \left({Y\over 2\exp(X)(\exp(X)-1)}\right)$$ ?