1. Tardigrade
  2. Question
  3. Mathematics
  4. If tan -1(x+1)+ cot -1(x-1)= sin -1((4/5))+ cos -1((3/5)), then x has the value

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $\tan ^{-1}(x+1)+\cot ^{-1}(x-1)=\sin ^{-1}\left(\frac{4}{5}\right)+\cos ^{-1}\left(\frac{3}{5}\right)$, then $x$ has the value

Inverse Trigonometric Functions

Solution:

$\tan ^{-1}\left(\frac{x+1+\frac{1}{x-1}}{1-\frac{x+1}{x-1}}\right)=2 \tan ^{-1}\left(\frac{4}{3}\right)=\pi+\tan ^{-1}\left(\frac{-24}{7}\right)$
$\Rightarrow x^2=\frac{48}{7} \Rightarrow x=4 \sqrt{\frac{3}{7}}$.