Thread: induction proof of de moivres formula

Is this correct and enough proof
is true so i put 1 and its true now ima prove for
now we can rewrite that ^k with a formula i cant remember as

and now i foctour out cos x and sin x

is this enough

You "can't remember"? You just wrote it two lines above!
For n a positive integer, yes, that will be a valid proof once you use trig identities to show how you got from to .

DeMoivre's formula is true for n any number, of course, not just positive integers. It would think the simplest way to prove it is to use the fact that .