Question

Find the principal value of the following:

`sec^-1(-sqrt2)`

Answer 1

Let `sec^-1(-sqrt2)=y`
Then,
`secy=-sqrt2`
We know that the range of the principal value branch is [0, π] - `{pi/2}`.
Thus,

`secy=-sqrt2=sec((3pi)/4)`

`=>y=(3pi)/4in[0,pi],y!=pi/2`

Hence, the principal value of `sec^-1(-sqrt2)    is    (3pi)/4.`