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The value of alpha so that sin^(-1)((2)/...

The value of `alpha` so that `sin^(-1)((2)/(sqrt(5)))`, `sin^(-1)((3)/(sqrt(10)))` and `sin^(-1)alpha` are the angles of a Delta is

A

`(1)/(2)`

B

`(sqrt(3))/(2)`

C

`(1)/(sqrt(2))`

D

`(1)/(sqrt(3))`

Text Solution

Verified by Experts

The correct Answer is:
C
`becausesin^(-1)((2)/(sqrt(5)))+sin^(-1)((3)/(sqrt(10)))+sin^(-1)alpha=pi`
`impliestan^(-1)(2)+tan^(-1)(3)+sin^(-1)alpha=pi`
`impliespi-tan^(-1)(1)+sin^(-1)(alpha)=piimpliesalpha=(1)/(sqrt(2))`
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