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If $\sin ^{-1}\left(\frac{x}{5}\right)+\operatorname{cosec}^{-1}\left(\frac{5}{4}\right)=\frac{\pi}{2}$ then a value of $x$ is
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The correct answer is:
$3$
$3$
$\sin ^{-1} \frac{x}{5}+\sin ^{-1} \frac{4}{5}=\frac{\pi}{2}$
$\Rightarrow \sin ^{-1} \frac{x}{5}=\cos ^{-1} \frac{4}{5} \Rightarrow \sin ^{-1} \frac{x}{5}=\sin ^{-1} \frac{3}{5}$
$\therefore x=3$.
$\Rightarrow \sin ^{-1} \frac{x}{5}=\cos ^{-1} \frac{4}{5} \Rightarrow \sin ^{-1} \frac{x}{5}=\sin ^{-1} \frac{3}{5}$
$\therefore x=3$.
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