Question

How do you find an expression for sin(x) in terms of eix and eix?

Answer 1

$e {}^{ix} = cos \: x + i \: sin \: x \\ e {}^{ - ix} = cos \: x - i \: sin \: x \\ e {}^{ix} - e {}^{ - ix } = 2i \: sin \: x \\ sin \: x = \frac{1}{2i} (e {}^{ix} - e {}^{ - ix} )$