Hyperbolic functions/R/Elementary properties/Fact/Proof/Exercise

Prove the following properties of the hyperbolic sine and the hyperbolic cosine

1. ${}\cosh x+\sinh x=e^{x}\,.$

2. ${}\cosh x-\sinh x=e^{-x}\,.$

3. ${}(\cosh x)^{2}-(\sinh x)^{2}=1\,.$

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