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Corollary: Representing Real Cosine by Complex Exponential Function
(related to Definition: Cosine of a Real Variable)
The cosine of a real variable \(\cos:\mathbb R\to \mathbb R\) can be represented by the exponential function of a complex variable by the following formula:
\[\cos(x)=\frac 12(\exp(ix)+\exp(ix)).\]
An alternative notation for this formula is
\[\cos(x)=\frac 12(e^{ix}+e^{ix}).\]
Table of Contents
Proofs: 1
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Proofs: 1 2
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References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983