Is $X^2-Y^2/ \sqrt{X^2+Y^2}$ normal where $X,Y\sim N(0,1)$
Given that $X,Y$ are independent $N(0,1)$ , show that $\frac{XY}{\sqrt{X^2+Y^2}},\frac{X^2-Y^2}{2\sqrt{X^2+Y^2}}$ are independent $N(0,\frac{1}{4})$