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The value of sin(1/4sin^(-1)(sqrt(63))/8...

The value of `sin(1/4sin^(-1)(sqrt(63))/8)` is `1/(sqrt(2))` (b) `1/(sqrt(3))` (c) `1/(2sqrt(2))` (d) `1/(3sqrt(3))`

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We have given
`sin(1/4sin^(-1)(sqrt(63))/8)`
Let `x=sin^(-1)(sqrt(63))/8`
`sinx=(sqrt(63))/8`
`cosx=(sqrt(64-63))/8=1/8`
`cos(x/2)=sqrt((1+cosx)/2)`
`cos(x/2)=sqrt((1/2)(9/8))`
`cos(x/2)=3/4`
...
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