The value of x satisfying `sin^(-1)(sqrt((3x-1)/(25)))+sin^(-1)(sqrt((3x+1)/(25)))=(pi)/(2)` lies in the interval

Options

A. (1,2)
B. (2,3)
C. (3,4)
D. (4,5)

Answer

D

Explanation

`sin^(-1)(sqrt((3x-1)/(25)))+sin^(-1)(sqrt((3x + 1)/(25)))=(pi)/(2)`
`rArr sin^(-1)(sqrt((3x-1)/(25)))=(pi)/(2)-sin^(-1)(sqrt((3x+1)/(25)))=cos^(-1)(sqrt((3x+1)/(25)))`
`rArr sin^(-1)(sqrt((3x-1)/(25)))=sin^(-1)(sqrt(1-(3x+1)/(25)))`
`rArr sin^(-1) (sqrt((3x-1)/(25)))=sin^(-1)(sqrt((24-3x)/(25)))`
`rArr (3x-1)/(25)=(24-3x)/(25)`
`rArr x = (25)/(6)`