If , find the value of…

MATHEMATICS · Subjective · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

If

\sin^{-1}x+\sin^{-1}y+\sin^{-1}z=\frac{3\pi}{2}

, find the value of

\displaystyle\sum_{\mathrm{cyc}}\frac{(x^{101}+y^{101})(x^{202}+y^{202})}{(x^{303}+y^{303})(x^{404}+y^{404})}

.

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