For any positive integer n , let S n : (0, ∞) → be defined by S_ n (x)= _ k=1 ^ n ^ -1 (…
Mathematics · JEE Advanced · NTA Exams — Trigonometry
For any positive integer n, let Sn : (0, ∞) → 
be defined by
\[S_{n}(x)=\sum_{k=1}^{n} \cot ^{-1}\left(\frac{1+k(k+1) x^{2}}{x}\right),\]
where for any x ∈
, cot–1(x) ∈ (0, π) and
\(\ an ^{-1}(x) \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) .\) Then which of the following statements is (are) TRUE?
be defined by \[S_{n}(x)=\sum_{k=1}^{n} \cot ^{-1}\left(\frac{1+k(k+1) x^{2}}{x}\right),\]
where for any x ∈
, cot–1(x) ∈ (0, π) and \(\ an ^{-1}(x) \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) .\) Then which of the following statements is (are) TRUE?
- The equation S3(x) =
- tan(Sn(x))
Answer
(A)
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