If \( (a+\sqrt{2} b \cos x)(a-\sqrt{2} b \cos y)=a^{2}-b^{2} \), where \( ab \) \( \mathrm{P} \)...

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

W)
[JEE Main-2020 (September)]
(1) \( \frac{2 a+b}{2 a-b} \)
(2) \( \frac{a-b}{a+b} \)
(3) \( \frac{a+b}{a-b} \)
(4) \( \frac{a-2 b}{a+2 b} \)
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