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If `cos^(-1)x+cos^(-1)y+cos^(-1)z=pi`, thenA. `x^(2)+y^(2)=z^(2)`B. `x^(2)+y^(2)+z^(2)=0`C. `x^(2)+y^(2)+z^(2)=1-2xyz`D. None of these |
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Answer» Correct Answer - C Given `cos^(-1)x+cos^(-1)y+cos^(-1)z=pi` `implies cos^(-1)(xy-sqrt(1-x^(2))sqrt(1-y^(2)))=pi-cos^(-1)z` `implies xy-sqrt(1-x^(2))sqrt(1-y^(2))=cos (pi-cos^(-1)z)` `=-cos(cos^(-1z))=0` `implies xy+z=sqrt(1-x^(2))sqrt(1-y^(2))` `implies x^(2)y^(2)+z^(2)+2xyz =(1-x^(2))(1-y^(2))` `=1-x^(2)-y^(2)+x^(2)y^(2)` `implies x^(2)+y^(2)+z^(2)=1-2xyz` |
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