Assertion : ^ -1 x- x^ 2 2 + x^ 3 4 - = d 2 - ^ -1 x^ 2 - x^ 4 2 + x^ 6 4 for 0 Reason …
Mathematics · JEE Advanced · NTA Exams — Sets, Relations and Functions
Assertion : \(\sin ^{-1}\left\{x-\frac{x^{2}}{2}+\frac{x^{3}}{4}-\ldots\right\}\)
\(=\frac{d}{2}-\cos ^{-1}\left\{x^{2}-\frac{x^{4}}{2}+\frac{x^{6}}{4} \ldots\right\}\) for 0 < |x| < \(\sqrt{2}\) has a unique solution.
Reason : \(\tan ^{-1} \sqrt{x(x+1)}+\sin ^{-1} \sqrt{x^{2}+x+1}=\frac{\pi}{2}\) has no solution for \(-\sqrt{2}\) < x < 0 .
\(=\frac{d}{2}-\cos ^{-1}\left\{x^{2}-\frac{x^{4}}{2}+\frac{x^{6}}{4} \ldots\right\}\) for 0 < |x| < \(\sqrt{2}\) has a unique solution.
Reason : \(\tan ^{-1} \sqrt{x(x+1)}+\sin ^{-1} \sqrt{x^{2}+x+1}=\frac{\pi}{2}\) has no solution for \(-\sqrt{2}\) < x < 0 .
- If Assertion is true, Reason is true, Reason is a correct explanation for Assertion.
- If Assertion is true, Reason is true, Reason is not a correct explanation for Assertion.
- If Assertion is true, Reason is false.
- If Assertion is false, Reason is true.
Answer
(C) If Assertion is true, Reason is false.
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