Question

Find the principal value of `sin^-1(1/sqrt2)`

Answer 1

Let `sin^-1(1/sqrt2)`

`∴ sin^-1x=(1/sqrt2)`

`∴ sin x= sin(pi/4)`

The principal value branch of

`sin^-1 "x"  "is" [-pi/2,pi/2] `

`sin^-1 (sin theta) = theta`

Hence, the required principal value of x is `pi/4`