The hyperbolic cosine function, denoted as cosh(x), is a mathematical function defined as the average of the exponential functions $e^x$ and $e^{-x}$, given by the formula $$ ext{cosh}(x) = rac{e^x + e^{-x}}{2}$$. It plays a key role in hyperbolic geometry and appears frequently in various mathematical contexts such as calculus and differential equations, particularly when dealing with hyperbolic functions.
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