I am having a little struggle with two questions about deMoivre's theorem and I did not find anything helpful in my books, so I was wondering if anyone here knew it.

First of all I assume that for those particalur questions

cos(pheta)= 1/2(z-1/z)

and

sin(pheta= 1/2i(z-1/z)

are given formulas? (if anyone knows?)

and finally I do not understand how to get from the step where I worked out all z's in my brackets to an answer that makes sense.

Thanks for your time and help