Question

How do you evaluate `arcsec (sec(-pi/3))`?

Answer 1

`pi/3`

First `sec(-pi/3)` would be equal to `sec(pi/3)` = 2. ( Angle -`pi/3` lies in the fourth quadrant and because cosine is positive there sec would also be positive).

Now the problem is reduced to evaluating arcsec2. Since `sec(pi/3)` is 2, hence arcsec2 would be equal to `pi/3`

Answer 2

`theta=arcsec(sec(-pi/3))`

`sectheta=sec(-pi/3)`

`:.theta=-pi/3`