S n n 1 2 1 tan … 3 3 – æ ö ç ÷ + è ø n n + + 1 1 tan 1 ( 19)( 20) – æ ö + ç ÷ è ø ++ + n n , then tan S is equal to :

Question:

$S=\tan ^{-1}\left(\frac{1}{n^{2}+n+1}\right)+\tan ^{-1}\left(\frac{1}{n^{2}+3 n+3}\right)+\ldots$

$+\tan ^{-1}\left(\frac{1}{1+(n+19)(n+20)}\right)$, then tan $S$ is equal to :

  1. $\frac{20}{401+20 n}$

  2. $\frac{n}{n^{2}+20 n+1}$

  3. $\frac{20}{n^{2}+20 n+1}$

  4. $\frac{n}{401+20 n}$


Correct Option: 3

JEE Main Previous Year 1 Question of JEE Main from Mathematics Inverse Trigonometric Functions chapter.
JEE Main Previous Year Online April 23, 2013

Solution:

Related Questions

  • If $\alpha=\cos ^{-1}\left(\frac{3}{5}\right), \beta=\tan ^{-1}\left(\frac{1}{3}\right)$, where $0<\alpha, \beta<\frac{\pi}{2}$, then $\alpha-\beta$ is equal to:

    View Solution

  • A value of $x$ satisfying the equation $\sin \left[\cot ^{-1}(1+x)\right]=\cos$ $\left[\tan ^{-1} x\right]$, is :

    View Solution

  • The principal value of $\tan ^{-1}\left(\cot \frac{43 \pi}{4}\right)$ is:

    View Solution

  • The number of solutions of the equation, $\sin ^{-1} x=2 \tan ^{-1} x$ (in principal values) is :

    View Solution

  • A value of $\tan ^{-1}\left(\sin \left(\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\right)\right.$ is

    View Solution

  • A value of $\tan ^{-1}\left(\sin \left(\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\right)\right.$ is

    View Solution

  • The largest interval lying in $\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)$ for which the function, $f(x)=4^{-x^{2}}+\cos ^{-1}\left(\frac{x}{2}-1\right)+\log (\cos x)$, is defined, is

    View Solution

  • The domain of the function $f(x)=\frac{\sin ^{-1}(x-3)}{\sqrt{9-x^{2}}}$ is

    View Solution

  • The trigonometric equation $\sin ^{-1} x=2 \sin ^{-1} a$ has a solution for

    View Solution

  • $$

    \cot ^{-1}(\sqrt{\cos \alpha})-\tan ^{-1}(\sqrt{\cos \alpha})=x

    $$ then $\sin x=$

    View Solution

Leave a Reply

Your email address will not be published.

error: Content is protected !!
Download App