The number of triple satisfying `sin^(-1)x+cos^(-1)y+sin^(-1)z=2pi` is

Options

A. 0
B. 2
C. 1
D. infinite

Explanation

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`