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If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi,t h ...

If `cos^(-1)x+cos^(-1)y+cos^(-1)z=pi,t h e n`

A

`x^(2)+y^(2)+z^(2)+2xyz=1`

B

`(sin^(-1)x+sin^(-1)y+sin^(-1)z)=cos^(-1)x+cos^(-1)y+cos^(-1)z`

C

`xy+yz+zx=x+y+z-1`

D

`(x+(1)/(x))+(y+(1)/(y))+(z+(1)/(z))ge6`

Text Solution

Verified by Experts

The correct Answer is:
A
`cos^(-1)x+cos^(-1)y+cos^(-1)z=pi`
`rArrsin^(-1)x+sin^(-1)y+sin^(-1)z=(pi)/(2)`
Also , `cos^(-1)x+cos^(-1)y=cos^(-1)(-z)`
`rArrxy-sqrt(1-x^(2))sqrt(1-y^(2))=-z`
`rArrx^(2)+y^(2)+z^(2)+2xyz=1`
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