# verify Euler's sine and cosine Identity

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• Dec 5th 2009, 01:34 PM
hotdogking
verify Euler's sine and cosine Identity
sine(x)= 1/2i(e^ix -e^-ix) and cos(x)=1/2i(e^ix + e^-ix)

I am supposed to verify these identities. I know that e^ix = cos x + i sin x.
So do I plug that in and simplify or is there something that I am missing?
• Dec 5th 2009, 01:39 PM
lvleph
Yes, plug that in and use some trig identities. The most useful one will be that $\sin (-x) = -\sin x \text{ and } \cos(-x) = \cos x$.