JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(y(x)=\cot ^{-1}\left(\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right), x \in\left(\frac{\pi}{2}, \pi\right)\) then \(\frac{d y}{d x}\) at \(x=\frac{5 \pi}{6}\) is:
- A \(-\frac{1}{2}\)
- B \(-1\)
- C \(\frac{1}{2}\)
- D \(0\)
Answer & Solution
Correct Answer
(A) \(-\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(y(x)=\cot ^{-1}\left[\frac{\cos \frac{x}{2}+\sin \frac{x}{2}+\sin \frac{x}{2}-\cos \frac{x}{2}}{\cos \frac{x}{2}+\sin \frac{x}{2}-\sin \frac{x}{2}+\cos \frac{x}{2}}\right]\) \(y(x)=\cot ^{-1}\left(\tan \frac{x}{2}\right)=\frac{\pi}{2}-\frac{x}{2}\)…
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