(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I want to show that:

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

2. Relevant equations

There is a trigonometric identity that says

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

3. 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]

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# Homework Help: Deriving arccos from arcsin

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