The value of cos left(sin ^{-1} frac{pi}{3}+c | vedclass

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(D) We know that the domain of $\sin ^{-1} x$ and $\cos ^{-1} x$ is $x \in [-1, 1]$.Here,the argument is $\frac{\pi}{3}$.Since $\pi \approx 3.14159$,w

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Does not exist

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(D) We know that the domain of $\sin ^{-1} x$ and $\cos ^{-1} x$ is $x \in [-1, 1]$.Here,the argument is $\frac{\pi}{3}$.Since $\pi \approx 3.14159$,we have $\frac{\pi}{3} \approx 1.047$.Because $1.047 > 1$,the value $\frac{\pi}{3}$ lies outside the domain $[-1, 1]$.Therefore,$\sin ^{-1} \left(\frac{\pi}{3}\right)$ and $\cos ^{-1} \left(\frac{\pi}{3}\right)$ are not defined in the set of real numbers.Thus,the expression $\cos \left(\sin ^{-1} \frac{\pi}{3}+\cos ^{-1} \frac{\pi}{3}\right)$ does not exist.

The value of $\cos \left(\sin ^{-1} \frac{\pi}{3}+\cos ^{-1} \frac{\pi}{3}\right)$ is

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