What is the "Book proof" of Euler's formula?

[VKnopp]

The eccentric mathematician Paul Erdos believed in a deity known as the SF (supreme fascist). He believed the SF teased him by hiding his glasses, hiding his Hungarian passport and keeping mathematical truths from him. He also believed that the SF has a book that consists of all the most elegant, beautiful, simple proofs to every theorem.

There are many proofs for Euler's formula,

$e^{it}=\cos(t)+isin(t)$

Which one would be the "Book proof"? Or the simplest, most elegant proof.

 

[micromass]

Depends on your definitions.

 

[jedishrfu]

There a book for that:

https://www.amazon.com/dp/3662442043/?tag=pfamazon01-20

 

[mathman]

When you identify these functions with their power series, you see the match.