- #1
metgt4
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Homework Statement
By considering the real and imaginary parts of the product eithetaeiphi, 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
ei(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