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tanh x = sinh x cosh x = e x − e − x e x + e − x = displaystyle tanh x= frac sinh x cosh x = frac e^ x -e^ -x e^ x +e^ -x =
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Hyperbolic functions come about during the answers of numerous linear differential equations (as an example, the equation defining a catenary), of some cubic equations, in calculations of angles and distances in hyperbolic geometry, and of Laplace's equation in this contact form Cartesian coordinates.
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e i x = cos x + i sin x e − i x = cos x − i sin x displaystyle get started aligned e^ ix &=cos x+i;sin xe^ -ix &=cos x-i;sin xconclude aligned