JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f(\mathrm{x})=\left(\sin \left(\tan ^{-1} \mathrm{x}\right)+\sin \left(\cot ^{-1} \mathrm{x}\right)\right)^{2}-1,|\mathrm{x}|>1\) If \(\frac{d y}{d x}=\frac{1}{2} \frac{d}{d x}\left(\sin ^{-1}(f(x))\right) \) and \( y(\sqrt{3})=\frac{\pi}{6}\) then \(y(-\sqrt{3})\) is equal to
- A \(\frac{5 \pi}{6}\)
- B \(-\frac{\pi}{6}\)
- C \(\frac{\pi}{3}\)
- D \(\frac{2\pi}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{5 \pi}{6}\)
Step-by-step Solution
Detailed explanation
Let \(\tan ^{-1} \mathrm{x}=\theta, \theta \in\left(-\frac{\pi}{2},-\frac{\pi}{4}\right) \cup\left(\frac{\pi}{4}, \frac{\pi}{2}\right)\) \(f(x)=(\sin \theta+\cos \theta)^{2}-1=\sin 2 \theta=\frac{2 x}{1+x^{2}}\) Now,…
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