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

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Question

(A) Given the equation: $\sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right)=1$We know that $\sin \left(\frac{\pi}{2}\right) = 1$. Therefore,we can

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$\frac{1}{5}$

Vedclass · Answer

(A) Given the equation: $\sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} xight)=1$We know that $\sin \left(\frac{\pi}{2}ight) = 1$. Therefore,we can write:$\sin ^{-1} \frac{1}{5} + \cos ^{-1} x = \frac{\pi}{2}$We also know the identity $\sin ^{-1} 	heta + \cos ^{-1} 	heta = \frac{\pi}{2}$ for $	heta \in [-1, 1]$.Comparing $\sin ^{-1} \frac{1}{5} + \cos ^{-1} x = \sin ^{-1} \frac{1}{5} + \cos ^{-1} \frac{1}{5}$,we get:$x = \frac{1}{5}$

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

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