markusername8 markusername8
  • 21-05-2018
  • Mathematics
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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 Eulers formula to write eitheta and eitheta in terms of sine and cosine Then subtract them class=

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LammettHash
LammettHash LammettHash
  • 21-05-2018
Euler's formula tells us that

[tex]e^{i\theta}=\cos\theta+i\sin\theta[/tex]
[tex]e^{-i\theta}=\cos\theta-i\sin\theta[/tex]

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

[tex]e^{i\theta}-e^{-i\theta}=i\sin\theta-(-i\sin\theta)=2i\sin\theta[/tex]

Divide both sides by [tex]2i[/tex] and you're done.
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