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If x ,\ y ,\ z in [-1,1] such that cos^(...

If `x ,\ y ,\ z in [-1,1]` such that `cos^(-1)x+cos^(-1)y+cos^(-1)z=0` , find `x+y+z` .

A

`-3`

B

3

C

0

D

`3 pi`

Text Solution

Verified by Experts

The correct Answer is:
B
We have
`x,y,z in[-1,1]`
`rarr -1lexle1-1leyle1,-1lezle1`
`rarr 0lecos^(-1)xlepi0lecos^(-1)ylepi,0lecos^(-1)zlepi`
`therefore cos^(-1)x+cos^(-1)y+cos^(-1)z=0`
`rarr cos^(-1)x=0, cos^(-1)y=0 and cos^(-1)z=0`
`rarr x=y=z=3`
Hence x+y+z=3
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