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Question:

If $\sin ^{-1}\left(\frac{1}{3}\right)+\cos ^{-1} x=\frac{\pi}{2}$, then find $x$

Solution:

We know that $\sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2}$.

We have

$\sin ^{-1}\left(\frac{1}{3}\right)+\cos ^{-1} x=\frac{\pi}{2}$

$\Rightarrow \sin ^{-1}\left(\frac{1}{3}\right)=\frac{\pi}{2}-\cos ^{-1} x$

$\Rightarrow \sin ^{-1}\left(\frac{1}{3}\right)=\sin ^{-1} x$

$\Rightarrow x=\frac{1}{3}$

$\therefore x=\frac{1}{3}$

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