Question

For the principal value, evaluate the following:

`sec^-1(sqrt2)+2\text{cosec}^-1(-sqrt2)`

Answer 1

`sec^-1(sqrt2)+2cosec^-1(-sqrt2)=sec^-1(sec  pi/4)+2cosec^-1[cosec(-pi/4)]`

`=pi/4-2xxpi/4`

`=pi/4-pi/2`

`=-pi/4`