JEE Math Practice Question

If $$\left( {a + \sqrt 2 b\cos x} \right)\left( {a - \sqrt 2 b\cos y} \right) = {a^2} - {b^2}$$ where a > b > 0, then $${{dx} \over {dy}}\,\,at\left( {{\pi \over 4},{\pi \over 4}} \right)$$ is :

1. A.$${{a - 2b} \over {a + 2b}}$$
2. B.$${{a - b} \over {a + b}}$$
3. C.$${{a + b} \over {a - b}}$$
4. D.$${{2a + b} \over {2a - b}}$$