If sin left(sin ^{-1} frac{1}{5}+cos ^{-1} xr | vedclass

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(A) Given the equation: $\sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right)=1$ Taking $\sin ^{-1}$ on both sides: $\sin ^{-1} \frac{1}{5}+\cos ^{-1

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$\frac{1}{5}$

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(A) Given the equation: $\sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} xight)=1$ Taking $\sin ^{-1}$ on both sides: $\sin ^{-1} \frac{1}{5}+\cos ^{-1} x = \sin ^{-1}(1)$ Since $\sin ^{-1}(1) = \frac{\pi}{2}$,we have: $\sin ^{-1} \frac{1}{5}+\cos ^{-1} x = \frac{\pi}{2}$ We know the identity $\sin ^{-1} 	heta + \cos ^{-1} 	heta = \frac{\pi}{2}$ for $	heta \in [-1, 1]$. Comparing the two equations,we get: $\cos ^{-1} x = \cos ^{-1} \frac{1}{5}$ Therefore,$x = \frac{1}{5}$.

If $\sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right)=1$,then the value of $x$ is

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