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sin(1/4sin^(- 1)(sqrt 63/8)i s...

`sin(1/4sin^(- 1)(sqrt 63/8)i s`

A

`(1)/(2)`

B

`(1)/(3)`

C

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

D

`(1)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
C
We have sin `((1)/(4)"sin"^(-1)(sqrt(63))/(8))`
Let `"sin"^(-1)(sqrt(63))/(8)=theta`
`therefore (sqrt(63))/(8)=sin theta`
`rArr cos. theta = (1)/(8)`
`therefore cos.(theta)/(2)=sqrt((1+cos theta)/(2))=sqrt((1+(1)/(8))/(2))=(3)/(4)`
`rArr = sin.(theta)/(4)=sqrt((1-cos.(theta)/(2))/(2))=sqrt((1-(3)/(4))/(2))=(1)/(2sqrt(2))`
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