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$If \sin^{- 1} x + \sin^{- 1} y + \sin^{- 1} z = \frac{3 π}{2}$ then the value of $x^{100} + y^{100} + z^{100} - \frac{3}{x^{101} + y^{101} + z^{101}}$ is

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Correct option is C

We have sin–1x + sin–1y + sin–1z = 3π2 it is possible only whensin−1⁡x=π2⇒x=1 ∵sin−1⁡x≤π2sin−1⁡y=π2⇒y=1; sin−1⁡z=π2⇒z=1∴x100+y100+z100−3x101+y101+z101=1+1+1−33=3−1=2

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If sin−1⁡x+sin−1⁡y+sin−1⁡z=3π2 then the value of x100+y100+z100−3x101+y101+z101 is

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$If \sin^{- 1} x + \sin^{- 1} y + \sin^{- 1} z = \frac{3 π}{2}$ then the value of $x^{100} + y^{100} + z^{100} - \frac{3}{x^{101} + y^{101} + z^{101}}$ is