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?

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- Dec 5th 2009, 12:34 PMhotdogkingverify 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, 12:39 PMlvleph
Yes, plug that in and use some trig identities. The most useful one will be that $\displaystyle \sin (-x) = -\sin x \text{ and } \cos(-x) = \cos x$.