- #1

Nathanael

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## Homework Statement

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There is an exercise which says "Show that cos(ix)=cosh(x)"

**2. The attempt at a solution**

The only thing I can think of is that cos(ix) is a solution to y''=y with initial conditions y(0)=1 and y'(0)=0 therefore cos(ix)=cosh(x)

There's no solution given, but it is from a chapter on complex numbers from a calculus book, so I don't think knowledge of differential equations is expected, so I doubt this is the solution they were going for.

Does anyone have another method? Perhaps you can some how use [itex]e^{i\theta}= \cos \theta+i \sin \theta[/itex] ? I can't think of a way.