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If "sin"^(-1)(1)/(3)+"sin"^(-1)(2)/(3)=s...

If `"sin"^(-1)(1)/(3)+"sin"^(-1)(2)/(3)=sin^(-1)x`, then the value of x is

A

0

B

`((sqrt(5)-4sqrt(2)))/(9)`

C

`((sqrt(5)+4sqrt(2)))/(9)`

D

`(pi)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given that , `"sin"^(-1)(1)/(3)+"sin"^(-1)(2)/(3)="sin"^(-1)x`
`rArrsin^(-1)((1)/(3)sqrt(1-(4)/(9))+(2)/(3)sqrt(1-(1)/(9)))=sin^(-1)x`
`rArrsin^(-1)((1)/(3)*(sqrt(5))/(3)+(2)/(3)*(sqrt(8))/(3))=sin^(-1)x`
`rArrsin^(-1)((sqrt(5)+4sqrt(2))/(9))=sin^(-1)x`
`thereforex=((sqrt(5)+4sqrt(2))/(9))`
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