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If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi, sho...

If `sin^(-1)x+sin^(-1)y+sin^(-1)z=pi`, show that `x^4+y^4+z^4+4x^2y^2z^2=2(x^2y^2+y^2z^2+z^2x^2)`

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`sin^-1x+sin^-1y +sin^-1z = pi`
`=> sin^-1x+sin^-1y = pi - sin^-1z`
`=> sin^-1(xsqrt(1-y^2)+ysqrt(1-x^2)) = pi-sin^-1z`
Taking sin both sides,
`=> sin(sin^-1(xsqrt(1-y^2)+ysqrt(1-x^2))) = sin(pi- sin^-1z)`
`=> xsqrt(1-y^2)+ysqrt(1-x^2) =z`
`=> xsqrt(1-y^2) =z - ysqrt(1-x^2)`
Taking square both sides,
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