Solve for x :
Question:

Solve for x :

$\tan ^{-1} x=\sin ^{-1} \frac{1}{\sqrt{2}}$

Solution:

To find: value of x

Given: $\tan ^{-1} \mathrm{X}=\sin ^{-1} \frac{1}{\sqrt{2}}$

We know that $\sin \frac{\pi}{4}=\frac{1}{\sqrt{2}}$

Therefore, $\frac{\pi}{4}=\sin ^{-1} \frac{1}{\sqrt{2}}$

Substituting in the given equation,

$\tan ^{-1} x=\frac{\pi}{4}$

$x=\tan \frac{\pi}{4}$

$\Rightarrow x=1$

Therefore, x = 1 is the required value of x.