If ^ -1 (3 )+ ^ -1 x= 2 , find x. - Vidyadip

Question

If $\tan^{-1}\big(\sqrt{3}\big)+\cot^{-1}\text{x}=\frac{\pi}{2},$ find x.

✓

Answer

We know that $\tan^{-1}\text{x}+\cot^{-1}\text{x}=\frac{\pi}{2} $
We have
$\Rightarrow\tan^{-1}\big(\sqrt3\big)+\cot^{-1}\text{x}=\frac{\pi}{2}$
$ \Rightarrow\tan^{-1}\big(\sqrt3\big)=\frac{\pi}{2}-\cot^{-1}\text{x}$
$ \Rightarrow\tan^{-1}\big(\sqrt3\big)=\tan^{-1}\text{x}$
$\Rightarrow\text{x}=\sqrt3$

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