If sin^{-1} x = frac{pi}{5} for some x in (-1 | vedclass

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(A) We know the identity for inverse trigonometric functions: $\sin^{-1} x + \cos^{-1} x = \frac{\pi}{2}$ for all $x \in [-1, 1]$.Given that $\sin^{-1

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$\frac{3\pi}{10}$

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(A) We know the identity for inverse trigonometric functions: $\sin^{-1} x + \cos^{-1} x = \frac{\pi}{2}$ for all $x \in [-1, 1]$.Given that $\sin^{-1} x = \frac{\pi}{5}$.Substituting this value into the identity,we get: $\frac{\pi}{5} + \cos^{-1} x = \frac{\pi}{2}$.Therefore,$\cos^{-1} x = \frac{\pi}{2} - \frac{\pi}{5}$.Taking the least common multiple $(LCM)$ of $2$ and $5$,which is $10$,we get: $\cos^{-1} x = \frac{5\pi - 2\pi}{10} = \frac{3\pi}{10}$.

If $\sin^{-1} x = \frac{\pi}{5}$ for some $x \in (-1, 1)$,then the value of $\cos^{-1} x$ is

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