Question:
If $\tan ^{-1}(\sqrt{3})+\cot ^{-1} x=\frac{\pi}{2}$, find $x$
Solution:
We know that $\tan ^{-1} x+\cot ^{-1} x=\frac{\pi}{2}$.
We have
$\tan ^{-1}(\sqrt{3})+\cot ^{-1} x=\frac{\pi}{2}$
$\Rightarrow \tan ^{-1}(\sqrt{3})=\frac{\pi}{2}-\cot ^{-1} x$
$\Rightarrow \tan ^{-1}(\sqrt{3})=\tan ^{-1} x$
$\Rightarrow x=\sqrt{3}$
$\therefore x=\sqrt{3}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.