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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