Here

there's the proof of a very nice trigonometric identity. is there a way to generate other identities that are similar to this-one by using also the complex numbers ?

thanks, p.

Pascal,

There are plenty of ways to generate identities. Here's a simple one:

To express powers of $\cos \theta$ in terms of $\cos \theta$, $\cos 2\theta$ etc.:

Consider ${\cos }^3\theta$as an example:

${\cos }^3\theta =[1/2(e^{(i\theta )}+e^{-i\theta }{)]}^3$

$=1/4[1/2(e^{3i\theta }+e^{-3i\theta })+3/2(e^{i\theta }+e^{-i\theta })]$

$=1/4[\cos 3\theta +3\cos \theta ]$

The method works for other powers of $\cos \theta$, and can similarly be applied to powers of $\sin \theta$.

It can also be applied in reverse to express $\cos n\theta$ in terms of powers of $\cos \theta$.
Andre