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

• A

  $\frac{a+b}{a-b}$
• Correct answer
  B

  $\frac{a-b}{a+b}$
• C

  $\frac{a-2 b}{a+2 b}$
• D

  $\frac{2 a+b}{2 a-b}$

Hence, the correct answer is option: 'B'.