Prove Standard Formulae for cos(theta+phi) & sin(theta+phi)

[metgt4]

Homework Statement

By considering the real and imaginary parts of the product e^ithetae^iphi, prove the standard formulae for cos(theta+phi) and sin(theta+phi)

Homework Equations

The standard formula for:
cos(theta+phi) = cos(theta)cos(phi) - sin(theta)sin(phi)
sin(theta+phi) = sin(theta)cos(phi) + sin(phi)cos(theta)

The Attempt at a Solution

from hereon out, let's let t=theta and p=phi. I can't figure out how to put the symbols in there on this site

e^i(t+p) = [cos(t) + isin(t)] [cos(p) + isin(p)]

= cos(t)cos(p) - sin(t)sin(p) + isin(t)cos(p) + isin(p)cos(t)

REAL PART = cos(t)cos(p) - sin(t)sin(p)
IMAGINARY PART = isin(t)cos(p) + isin(p)cos(t)

but I can't use the trig identities because I have to prove them. I'm probably not going in the right direction, but if somebody could point me in the right way, that would be great!

Thanks!
Andrew

 

[Matterwave]

You could then expand $$e^{i(\phi+\theta)}=cos(\phi+\theta)+isin(\phi+\theta)$$ by just considering phi+theta to be collectively x in the Euler's formula. If you match the real and imaginary parts you should get the correct trig identities.