Double integration with substitution

Use substitution to find $\displaystyle \int \int \cos (\frac{x-y}{x+y})dx dy$ over region D, where D is the triangle with vertices (0,0), (0,1), (1,0).

I think the required integral would then be the following, but have no clue as to what substitution is required.

$\displaystyle \int_0^1 \int_0^{1-x} \cos (\frac{x-y}{x+y})dy dx$

I would like someone to check that my limits are correct and then point me in the right direction for a substitution, explaining how I should have come up with it. Thanks!