Thread: De Moivre's Theorum

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

What have you tried so far?

Why

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

?

Originally Posted by Vlasev

What have you tried so far?

I have tried subbing in the tan x=(z-z^-1)i(z+z^-1) into the equation and then expnding after that i decided because it wasnt the same as the (z^2+z^-2)/2 i put (cos x)^2+(sin x)^2=1 into the place were the 1 then expanded its equivilant de moivre's equation being Sin x=(z^1-z^-1)/2 and cos x= (z^1+z^-1)/2
but this did not help in achieving the other sides equation.

How did you sub in tan(x)?

Have you tried using DeMoivre's theorem?