Question

Find the principal value of `sec^-1 (- sqrt(2))`.

Answer 1

Let y = `sec^-1 (- sqrt(2))`

Where 0 ≤ y ≤ π

sec y = `- sqrt(2)`

`y +- pi/2`

`1/sec y = - 1/sqrt(2)` 

cos y = `- 1/sqrt(2)`

∴ The principal value of `sec^-1 (- sqrt(2)) = (3pi)/4`