if cos^(-1)((2)/(3x))+cos^(-1)((3)/(4x))...

if `cos^(-1)((2)/(3x))+cos^(-1)((3)/(4x))=(pi)/2, x>3/4` then `x=` (a) `(sqrt(145))/(11)` (b) `(sqrt(145))/(12)` (c) `(sqrt(146))/(10)` (d) `(sqrt(146))/(11)`

A

`(sqrt(45))/11`

B

`(sqrt(145))/10`

C

`(sqrt(146))/12`

D

`(sqrt(145))/12`

Text Solution

Verified by Experts

The correct Answer is:

D

`cos^(-1)(2//3x)=sin^(-1)(3//4x)impliessin^(-1)sqrt(1-4/(9x^(2)))=sin^(-1)(3//4x){2/(3x)gt0}`
`implies1-4/(9x^(2))=(9/16x^(2))=x^(2)=145/144`

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