Suppose that $\displaystyle X$ and $\displaystyle Y$ are independent standard normal random variables ~ N(0, 1).

What are the distributions of the following transformations?

1. $\displaystyle \frac{X^{2} - Y^{2}}{\sqrt{X^2 + Y^2}}$

2. $\displaystyle \frac{2XY}{\sqrt{X^2 + Y^2}}$

Are they independent?

Thanks in advance,