Math Help - Correlation

1. Correlation

$X$ and $Y$ are random variables with expectation equal to zero and variances $\sigma^2$ and $\omega^2\sigma^2$ respectively.
a) If $X$ and $Y$ are independent show that the correlation of $X+Y$ and $X-Y$ is

$\frac{1-\omega^2}{1+\omega^2}$.

b) Find the corresponding correlation if $X$ and $Y$ are not independent but have correlation $\rho$.

2. how about starting with the defintion of correlation in terms of covariance?