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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Aicharya · Accepted Answer

$\begin{aligned} & \sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2}=\frac{\pi}{2}+\frac{\pi}{2}+\frac{\pi}{2}=\sin ^{-1}(1)+\sin ^{-1}(1)+\sin ^{-1}(1) \ & \Rightarrow x=y=z=1 \ & \Rightarrow x^{100}+y^{100}+z^{100}=1^{100}+1^{100}+1^{100}=3\end{aligned}$

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

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