MHT CET · Maths · Inverse Trigonometric Functions
\(\cot ^{-1}\left(2 \cdot 1^2\right)+\cot ^{-1}\left(2 \cdot 2^2\right)+\cot ^{-1}\left(2 \cdot 3^2\right)+\ldots \ldots \ldots \ldots \ldots \ldots \ldots \infty =\)
- A \(\frac{\pi}{2}\)
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{4}\)
- D \(\overline{8}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
\(\sum_{n=1}^{\infty} \cot^{-1}(2n^2) = \sum_{n=1}^{\infty} \tan^{-1}\left(\frac{1}{2n^2}\right)\) \(= \sum_{n=1}^{\infty} \tan^{-1}\left(\frac{2}{4n^2}\right)\)
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