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Prove the following with Euler's formula to write e^itheta and e^-itheta in terms of sine and cosine. Then subtract them.

Prove the following with Euler's formula to write e^itheta and e^-itheta in terms-example-1

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Euler's formula tells us that


e^(i\theta)=\cos\theta+i\sin\theta

e^(-i\theta)=\cos\theta-i\sin\theta

Suppose we subtract the two. This eliminates the cosine terms.


e^(i\theta)-e^(-i\theta)=i\sin\theta-(-i\sin\theta)=2i\sin\theta

Divide both sides by
2i and you're done.
User Luiscarlostic
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