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The value of sin^(-1)((2sqrt(2))/(3))+si...

The value of `sin^(-1)((2sqrt(2))/(3))+sin^(-1)((1)/(3))` is

A

`(pi)/(4)`

B

`(pi)/(6)`

C

`(2pi)/(3)`

D

`(pi)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`sin^(-1)((2sqrt(2))/(3))+"sin"^(-1)(1)/(3)`
`=sin^(-1)((2sqrt(2))/(3))+cos^(-1)sqrt(1-((1)/(3))^(2))`
`=sin^(-1)((2sqrt(2))/(3))+cos^(-1)((2sqrt(2))/(3))=(pi)/(2)`
`[becausesin^(-1)x+cos^(-1)x=(pi)/(2)]`
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