Hey I am fairly new to this forum and am in need of some assistance I've been set a question which will most likely be on my next exam although the teacher will probably show me how to do this question with in the next few days I'm rather keen to see how to do it. Ive tried several times and haven't got the answers out.

Question:

If tan x=(z-z^-1)/i(z+z^-1) prove that cos 2x=(1-(tan x)^2)/(1+(tan x)^2)

Using De Moivre's Theorem

Useful information: cos 2x= (z^2+z^-2)/2

Sin 2x=(z^2-z^-2)/2i

and maybe (cos x)^2+(sin x)^2=1