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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:

$$x={Y^2\over 4\exp (2X)}+(\exp (X)-1)^2$$

$$y=\arctan \left({Y\over 2\exp(X)(\exp(X)-1)}\right)$$ ?

1 Answers 1