Complex analysis of Euler identities

First of all, the Taylor formula is introduced, and its essence is to use a function near the point, while the past derivative resembles the function value of the point.

Next, the Taylor formula for trigonometric functions at x=0 (sin (0) =0,cos (0) =1)

Sin (x) '	Sin (x) "	Sin (x) "	Sin (x) ""	Cos (x) '	Cos (x) "	Cos (x) "	Cos (x) ""
Cos (x)	-sin (x)	-cos (x)	Sin (x)	-sin (x)	-cos (x)	Sin (x)	Cos (x)
1	0	-1	0	0	-1	0	1

Can know the following conclusions. namely Taylor identity

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Complex analysis of Euler identities