The two variates $x$ and $y$ are uncorrelated and have standard deviation $ \sigma_x$ and $ \sigma_y$ respectively, the correlation coefficient between $x+y\: and \: x-y$ is

Question

$\begin {array} {1 1} (A)\;\large\frac{\sigma_x \sigma_y}{\sigma_x^2+\sigma_y^2} & \quad (B)\;\large\frac{1}{2}\bigg( \large\frac{1}{\sigma_x}+\large\frac{1}{\sigma_y} \bigg) \\ (C)\;\large\frac{\sigma_x^2-\sigma_y^2}{\sigma_x^2+\sigma_y^2} & \quad (D)\;None \: of \: these \end {array}$