![calculus - How can I evaluate $\lim_{n\to\infty}\Big[ \cot(\pi\sqrt{100n^2+n+1}\Big]$ - Mathematics Stack Exchange calculus - How can I evaluate $\lim_{n\to\infty}\Big[ \cot(\pi\sqrt{100n^2+n+1}\Big]$ - Mathematics Stack Exchange](https://i.stack.imgur.com/jX1Av.jpg)
calculus - How can I evaluate $\lim_{n\to\infty}\Big[ \cot(\pi\sqrt{100n^2+n+1}\Big]$ - Mathematics Stack Exchange
cot(π/4 - 2 cot^-1 3) = A. 4 B. 6 C. 5 D. none of these - Sarthaks eConnect | Largest Online Education Community
cot (π/4 - 2 cot^ -1 (3)) = (a) 7 (b) 6 (c) 5 (d) None of these - Sarthaks eConnect | Largest Online Education Community
![Let prod(r=1)^51 tan(pi/3(1+(3^r)/(3^(50)-1))=prod(r=1)^51 cot(pi/3(1+(3 ^r)/(3^(50)-1))]) On solving equation we get, 1-3 tan^2 (1+(3^r)/(3^(50)-1))=a/(bk-1),(a,b in I) then value of (a-b) is equal Let prod(r=1)^51 tan(pi/3(1+(3^r)/(3^(50)-1))=prod(r=1)^51 cot(pi/3(1+(3 ^r)/(3^(50)-1))]) On solving equation we get, 1-3 tan^2 (1+(3^r)/(3^(50)-1))=a/(bk-1),(a,b in I) then value of (a-b) is equal](https://d10lpgp6xz60nq.cloudfront.net/web-thumb/646353169_web.png)