1. Tardigrade
  2. Question
  3. Mathematics
  4. If 3 tan-1x+ cot-1x=π then x is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $3\, \tan^{-1}x+\cot^{-1}x=\pi$ then $x$ is equal to

KCETKCET 2016Inverse Trigonometric Functions

Solution:

Solution: We have $3 \tan ^{-1} x+\cot ^{-1} x=\pi$
$\Rightarrow 2 \tan ^{-1} x+\tan ^{-1} x+\cot ^{-1} x=\pi$
$\Rightarrow 2 \tan ^{-1} x+\frac{\pi}{2}=\pi $
${\left[\because \tan ^{-1} x+\cot ^{-1} x=\frac{\pi}{2}\right]} $
$\Rightarrow 2 \tan ^{-1} x=\pi-\frac{\pi}{2}$
$\Rightarrow 2 \tan ^{-1} x=\frac{\pi}{2}$
$\Rightarrow \tan ^{-1} x=\frac{\pi}{4} $
$\Rightarrow x=\tan \frac{\pi}{4} $
$\therefore x=1$