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schapman22
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Homework Statement
Use Euler's identity to prove that cos(u)cos(v)=(1/2)[cos(u-v)+cos(u+v)]
and sin(u)cos(v)=(1/2)[sin(u+v)+sin(u-v)]
Homework Equations
eui=cos(u) + isin(u)
e-ui=cos(u)-isin(u)
The Attempt at a Solution
I was able to this with other trig identities with no problem but this one I have hit a wall.
we are supposed to start with e(u+v)i+e(u-v)i=eu(evi+e-vi) which becomes.
cos(u+v)+isin(u+v)+cos(u-v)+isin(u-v)=eu(cos(v)+isin(v)+cos(v)-isin(v)) then
equating the real parts
cos(u+v)+cos(u-v)=eu(2cos(v)) then divide by 2
(1/2)[cos(u+v)+cos(u-v)]=eu(cos(v))
I cannot figure out why I have an eu and not a cos(u). Does anyone see where I have gone wrong or what I am missing? Thank you in advance.