If `sin^(-1)(3/x)+sin^(-1)(4/x)=pi/2`, then x is

Options

A. 3
B. 5
C. 7
D. 11

Explanation

We have
`sin^(-1)(3)/(x)+sin^(-1)(4)/(x)=(pi)/(2)`
`rarr sin^(-1)(3)/(x)=(pi)/(2)-sin^(-1)(4)/(x)`
`rarr sin^(-1)(3)/(x)=cos^(-1)(4)/(x)`
`rarr sin^(-1) (3)/(x)=sin^(-1)(sqrt(x^(2)-16)/(x))`
`rarr(3)/(x)=sqrt(x^(2))=-16)/(x)rarrx=5`