Difference between revisions of "Relationship between cos and cosh"
From specialfunctionswiki
| Line 5: | Line 5: | ||
==Proof== | ==Proof== | ||
| + | From the definition of $\cosh$ and the definition of $\cos$, | ||
| + | $$\cosh(iz)=\dfrac{e^{iz}+e^{-iz}}{2}=\cos(z),$$ | ||
| + | as was to be shown. | ||
==References== | ==References== | ||
[[Category:Theorem]] | [[Category:Theorem]] | ||
| − | [[Category: | + | [[Category:Proven]] |
Latest revision as of 03:48, 8 December 2016
Theorem
The following formula holds: $$\cos(z)=\cosh(iz),$$ where $\cos$ is the cosine and $\cosh$ is the hyperbolic cosine.
Proof
From the definition of $\cosh$ and the definition of $\cos$, $$\cosh(iz)=\dfrac{e^{iz}+e^{-iz}}{2}=\cos(z),$$ as was to be shown.
