With reference to the principal values,if sin | vedclass

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(B) The principal value range of $\sin ^{-1} x$ is $[-\frac{\pi}{2}, \frac{\pi}{2}]$.Given that $\sin ^{-1} x + \sin ^{-1} y + \sin ^{-1} z = \frac{3

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$3$

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(B) The principal value range of $\sin ^{-1} x$ is $[-\frac{\pi}{2}, \frac{\pi}{2}]$.Given that $\sin ^{-1} x + \sin ^{-1} y + \sin ^{-1} z = \frac{3 \pi}{2}$.Since the maximum value of each $\sin ^{-1}$ term is $\frac{\pi}{2}$,the sum can only be $\frac{3 \pi}{2}$ if each term is individually equal to its maximum value.Therefore,$\sin ^{-1} x = \frac{\pi}{2}$,$\sin ^{-1} y = \frac{\pi}{2}$,and $\sin ^{-1} z = \frac{\pi}{2}$.This implies $x = \sin(\frac{\pi}{2}) = 1$,$y = \sin(\frac{\pi}{2}) = 1$,and $z = \sin(\frac{\pi}{2}) = 1$.Substituting these values into the expression $x^{100} + y^{100} + z^{100}$:$1^{100} + 1^{100} + 1^{100} = 1 + 1 + 1 = 3$.

With reference to the principal values,if $\sin ^{-1} x + \sin ^{-1} y + \sin ^{-1} z = \frac{3 \pi}{2}$,then $x^{100} + y^{100} + z^{100} =$

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