JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumTrigonometry118× since 2002The sum of the infinite series cot−1(74)+cot−1(194)+cot−1(394)+cot−1(674)+…\cot^{-1}\left(\tfrac{7}{4}\right)+\cot^{-1}\left(\tfrac{19}{4}\right)+\cot^{-1}\left(\tfrac{39}{4}\right)+\cot^{-1}\left(\tfrac{67}{4}\right)+\ldotscot−1(47)+cot−1(419)+cot−1(439)+cot−1(467)+… is:AOption A. π2+tan−1(12)\frac{\pi}{2}+\tan^{-1}\left(\frac{1}{2}\right)2π+tan−1(21)BOption B. π2−cot−1(12)\frac{\pi}{2}-\cot^{-1}\left(\frac{1}{2}\right)2π−cot−1(21)COption C. π2+cot−1(12)\frac{\pi}{2}+\cot^{-1}\left(\frac{1}{2}\right)2π+cot−1(21)DOption D. π2−tan−1(12)\frac{\pi}{2}-\tan^{-1}\left(\frac{1}{2}\right)2π−tan−1(21)CheckSkip · show solution
