A calculus problem by Jose Sacramento

Calculus Level 4

\[ \int_0^1 \int_0^{1-x} \cos \left( \dfrac{x-y}{x+y} \right) \, dy \; dx \]

If the integral above can be expressed as \( \dfrac {\sin A}B\), where \(A\) and \(B\) are both positive integers, find \(A+B\).

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