Question

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$Prove..$
${e}^{ix}=cos \: x +i \: sin \: x$



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Answer 1

Explanation:

You can prove this using Taylor's/Maclaurin's Series.

Explanation:

First write out the identities in Taylor's Series for sinx and cosx as well as ex.

sinx=x−x33!+x55!...

cosx=1−x22!+x44!...

ex=1+x+x22!+x33!+x44!...

Usually to prove Euler's Formula you multiply ex by i, in this case we will multiply ex by −i.

And we will end with e−ix thus it will be equal to...

1+(−ix)+(−ix)22!+(−ix)33!+(−ix)44!...

Expand...

1−ix−x22!−i

.

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HOPE IT HELPS YOU.

Answer 2

Answer:

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