Question Number 62010 by aliesam last updated on 13/Jun/19
$${if}\: \\ $$$$ \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} −\mathrm{2}{xyz}=\mathrm{1} \\ $$$${prove}\:{that} \\ $$$$ \\ $$$$\frac{{dx}}{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:+\:\frac{{dy}}{\sqrt{\mathrm{1}−{y}^{\mathrm{2}} }}\:+\:\frac{{dz}}{\sqrt{\mathrm{1}−{z}^{\mathrm{2}} }}\:=\:\mathrm{0} \\ $$