JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(f(x)=\sin \left(\cos ^{-1}\left(\frac{1-2^{2 x}}{1+2^{2 x}}\right)\right)\) and its first derivative with respect to \(x\) is \(-\frac{ b }{ a } \log _{ e } 2\) when \(x =1,\) where \(a\) and \(b\) are integers, then the minimum value of \(\left| a ^{2}- b ^{2}\right|\) is.........
- A \(373\)
- B \(481\)
- C \(426\)
- D \(524\)
Answer & Solution
Correct Answer
(B) \(481\)
Step-by-step Solution
Detailed explanation
\(f ( x )=\sin \left(\cos ^{-1}\left(\frac{1-2^{2 x }}{1+2^{2 x }}\right)\right)\) at \(x =1 ; 2^{2 x }=4\) for \(\sin \left(\cos ^{-1}\left(\frac{1- x ^{2}}{1+ x ^{2}}\right)\right)\) Let \(\tan ^{-1} x =\theta ; \theta \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\)…
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