JEE Mains · Maths · STD 12 - 5. continuity and differentiation
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
- A \(\frac{-2}{3}\)
- B \(\frac{2}{9}\)
- C \(-\frac{1}{3 \sqrt{3}}\)
- D \(\frac{-2}{3 \sqrt{3}}\)
Answer & Solution
Correct Answer
(B) \(\frac{2}{9}\)
Step-by-step Solution
Detailed explanation
\(f(x)=-\tan \left(\frac{x}{2}-\frac{\pi}{8}\right)\) \(f^{\prime}(x)=-\frac{1}{2} \sec ^2\left(\frac{x}{2}-\frac{\pi}{8}\right)\) \(f^{\prime \prime}(x)=-\sec ^2\left(\frac{x}{2}-\frac{\pi}{8}\right) \cdot \tan \left(\frac{x}{2} \frac{-\pi}{8}\right) \cdot \frac{1}{2}\)…
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