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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…

Q1

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

[JEE Main 2023, 08 Apr (Shift 1)]

a

\(\frac{2}{9}\)

b

\(\frac{-2}{3}\)

c

\(\frac{-1}{3 \sqrt{3}}\)

d

\(\frac{2}{3 \sqrt{3}}\)

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