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  4. The value of x which satisfies the equation tan-1 x=sin-1 ((3/√10)) is

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Q. The value of $x$ which satisfies the equation $tan^{-1} x=sin^{-1} \left(\frac{3}{\sqrt{10}}\right)$ is

Inverse Trigonometric Functions

Solution:

Given, $tan^{-1}\,x =sin^{-1} \left[\frac{3}{\sqrt{10}}\right]$
$\Rightarrow x =tan \left\{sin^{-1}\left[\frac{3}{\sqrt{10}}\right]\right\}=tan \left\{tan^{-1}\,3\right\}$
$\Rightarrow x=3$