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If sin^(- 1)(3/x)+sin^(- 1)(4/x)=pi/2 t...

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

A

3

B

5

C

7

D

11

Text Solution

Verified by Experts

The correct Answer is:
B
Given , `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)`
`rArr9=x^(2)-16`
`rArrx=+-5`
`thereforex=5`
`[because-5"not satisfies the given equation"]`
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