Question

Find the principal value of the following:

`sec^-1(2)`

Answer 1

Let `sec^-1(2)=y`
Then,
sec y = 2
We know that the range of the principal value branch is `[0,pi]-{pi/2}.`
Thus,
`secy=2=sec(pi/3)`

`=>y=pi/3in[0,pi],y!=pi/2`

Hence, the principal value of `sec^-1(2)   is    pi/3. `