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Number of triplets (x, y, z) satisfying ...

Number of triplets (x, y, z) satisfying `sin^(-1)x+cos^(-1)y+sin^(-1)z=2pi`, is :

A

0

B

2

C

1

D

infinite

Text Solution

Verified by Experts

We know that
`sin^(-1)xle(pi)/(2) sin^(-1)zle(pi)/(2) and cos^(-1) y le pi`
`therefore sin^(-1)x+cos^(-1)y+sin^(-1)zle2pi`
`rarr sub^(-1)x=(pi)/(2) cos^(-1)y=pi and sin^(-1) =(pi)/(2)`
`rarr x=1 , y=-1 =pi and sin^(-1) z=(pi)/(2)`
`rarr x =1 ,y =-1 and z=1`
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