Number of integral values of \( K \) for which the system of equations; \[ \begin{array}{l} \cos...

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Number of integral values of \( K \) for which the system of equations;
\[
\begin{array}{l}
\cos ^{-1} x+\left(\sin ^{-1} y\right)^{2}=\frac{K \pi^{2}}{4} \\
\left(\sin ^{-1} y\right)^{2} \cos ^{-1} x=\frac{\pi^{4}}{16}
\end{array}
\]
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