- #1

guildmage

- 25

- 0

## Homework Statement

I want to show that:

[tex] \arccos \,z= \left( -1 \right) ^{n+1} \arcsin \,z+\pi/2\, +n\pi [/tex]

## Homework Equations

There is a trigonometric identity that says

[tex] \arccos \,z= \pi/2\, -\arcsin \,z [/tex]

## The Attempt at a Solution

So far, I have come up to this

[tex] \arccos\,z=\pi/2\, -{\it i}\log\ \left( -iz+\sqrt {1-{z}^{2}} \right) [/tex]

What is left to show is that

[tex] \arcsin\, \left( -z \right) = \arcsin\,z [/tex]

My plan is to add the periodicity (is that the term?) later on since

[tex] -\cos\,z= \cos\ \left( z+\pi \right) [/tex]