The number of ordered triplets `(x,y,z)` satisfy the equation `(sin^(- 1)x)^2=(pi^2)/4+(sec^(- 1)y)^2+(tan^(- 1)z)^2`

Options

A. 2
B. 4
C. 6
D. 8

Answer

A

Explanation

`(sin^(-1)x)in[-(pi)/(2),(pi)/(2)]`
`therefore (sin^(-1)x)^(2)le (pi^(2))/(4)`
`(sec^(-1)y)^(2), (tan^(-1)z)^(2)ge 0`
`therefore R.H.S. ge (pi^(2))/(4)`
`therefore (sin^(-1)x)^(2)=(pi^(2))/(4)`
`therefore (sex^(-1)y)^(2)+(tan^(-1)z)^(2)=0`
or `sec^(-1)y=tan^(-1)z=0`
`therefore sin^(-1)x = pm(pi)/(2), y = 1, z = 0`