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Question

Let $f(x)=\frac{\sin x+\cos x-\sqrt{2}}{\sin x-\cos x}, x \in[0, \pi]-\left\{\frac{\pi}{4}\right\}$. Then $f\left(\frac{7 \pi}{12}\right) f^{\prime \prime}\left(\frac{7 \pi}{12}\right)$ is equal to

$\frac{2}{3 \sqrt{3}}$
$\frac{2}{9}$
$\frac{-1}{3 \sqrt{3}}$
$\frac{-2}{3}$

Solution

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