If $$sin$$−$$1x+$$$$sin$$−$$1y+$$$$sin$$−$$1z=$$π, then the value of $$x4+y4+z4+4x2y2z2x2y2+y2z2+z2x2$$ is

Let $$x=y=z=32$$. Then $$x4+y4+z4+4x2y2z2x2y2+y2z2+z2x2=3x4+4x63x4=3+4x23=2$$

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If $\sin^{- 1} x + \sin^{- 1} y + \sin^{- 1} z = π$ , then the value of $\frac{x^{4} + y^{4} + z^{4} + 4 x^{2} y^{2} z^{2}}{x^{2} y^{2} + y^{2} z^{2} + z^{2} x^{2}}$ is

Moderate

Solution

$L e t x = y = z = \frac{\sqrt{3}}{2} . T h e n \frac{x^{4} + y^{4} + z^{4} + 4 x^{2} y^{2} z^{2}}{x^{2} y^{2} + y^{2} z^{2} + z^{2} x^{2}} = \frac{3 x^{4} + 4 x^{6}}{3 x^{4}} = \frac{3 + 4 x^{2}}{3} = 2$

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