If sec-11+x2+cosec-11+y2y+cot-11/z=π then

sec-11+x2=α cosec-11+y2y=β tan-1x+tan-1y+tan-1z=π tan-1x+y+z-xyz1-xy-yz-zx=π ⇒ x+y+z=xyz

If sec-11+x2+cosec-11+y2y+cot-11/z=π then

sec-11+x2=α cosec-11+y2y=β tan-1x+tan-1y+tan-1z=π tan-1x+y+z-xyz1-xy-yz-zx=π ⇒ x+y+z=xyz

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If $\sec^{- 1} \sqrt{1 + x^{2}} + {cosec}^{- 1} \frac{\sqrt{1 + y^{2}}}{y} + \cot^{- 1} (1 / z) = π$ then

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x + y + z = 0

x + y + z = 1

x + y + z = xyz

x + y + z = 2

answer is C.

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$\sec^{- 1} \sqrt{1 + x^{2}} = α {cosec}^{- 1} \frac{\sqrt{1 + y^{2}}}{y} = β$

$\tan^{- 1} x + \tan^{- 1} y + \tan^{- 1} z = π \tan^{- 1} (\frac{x + y + z - xyz}{1 - xy - yz - zx}) = π \Rightarrow x + y + z = xyz$

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If sec-11+x2+cosec-11+y2y+cot-11/z=π then

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If $\sec^{- 1} \sqrt{1 + x^{2}} + {cosec}^{- 1} \frac{\sqrt{1 + y^{2}}}{y} + \cot^{- 1} (1 / z) = π$ then