Find the principal value of `sin^(-1)``(1/(sqrt(2)))`

Explanation

The principal value branch of `sin^(-1)x ` is `[(-pi)/(2),(pi)/(2)]`.
Let `sin^(-1)(1/sqrt(2))=x` where`(-pi)/(2) le x le (pi)/(2)`
`:.sinx=(1)/(sqrt(2))=sin.(pi)/(4)`
`:.x=(pi)/(4) ` [ also `(-pi)/(2) le (pi)/(4) le (pi)/(2)` ]
`:.` The principle value of `sin^(-1)(1/sqrt(2))` is `(pi)/(4)`.