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The value of x satisfying sin^(-1)(sqrt(...

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

A

(1,2)

B

(2,3)

C

(3,4)

D

(4,5)

Text Solution

Verified by Experts

The correct Answer is:
D
`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)`
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