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

Options

A. `(1)/(2)`
B. `(1)/(3)`
C. `(1)/(2sqrt(2))`
D. `(1)/(5)`

Answer

C

Explanation

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))`