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The value of $x$ which satisfies the equation $\tan ^{-1} x=\sin ^{-1}\left(\frac{3}{\sqrt{10}}\right)$ is
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Verified Answer
The correct answer is:
$3$
Given,
$\begin{aligned}
& \quad \tan ^{-1} x=\sin ^{-1}\left[\frac{3}{\sqrt{10}}\right] \\
& \text { Given, } \\
& \Rightarrow x=\tan \left\{\sin ^{-1}\left[\frac{3}{\sqrt{10}}\right]\right\}=\tan \left\{\tan ^{-1} 3\right\} \\
& \Rightarrow x=3 .
\end{aligned}$
$\begin{aligned}
& \quad \tan ^{-1} x=\sin ^{-1}\left[\frac{3}{\sqrt{10}}\right] \\
& \text { Given, } \\
& \Rightarrow x=\tan \left\{\sin ^{-1}\left[\frac{3}{\sqrt{10}}\right]\right\}=\tan \left\{\tan ^{-1} 3\right\} \\
& \Rightarrow x=3 .
\end{aligned}$
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