JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
If \(\cot ^{-1}(\alpha)=\cot ^{-1} 2+\cot ^{-1} 8+\cot ^{-1} 18\) \(+\cot ^{-1} 32+\ldots . .\) upto \(100\) terms, then \(\alpha\) is
- A \(1.01\)
- B \(1.00\)
- C \(1.02\)
- D \(1.03\)
Answer & Solution
Correct Answer
(A) \(1.01\)
Step-by-step Solution
Detailed explanation
\(\operatorname{Cot}^{-1}(\alpha)=\cot ^{-1}(2)+\cot ^{-1}(8)+\cot ^{-1}(18)+\ldots .\) \(=\sum_{n=1}^{100} \tan ^{-1}\left(\frac{2}{4 n^{2}}\right)\) \(=\sum_{n=1}^{100} \tan ^{-1}\left(\frac{(2 n+1)-(2 n-1)}{1+(2 n+1)(2 n-1)}\right)\)…
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