John Robbins
03/12/2023 · Junior High School
Prove the identity. \[ \cosh (x)+\sinh (x)=e^{x} \] First, use the definitions of the hyperbolic functions, and then simplify by combining the exponential terms. \[ \begin{aligned} \cosh (x)+\sinh (x) & =\frac{1}{2}\left(e^{x}+e^{-x}\right)+\frac{1}{2}(\square) \\ & =\frac{1}{2}(\square) \\ & =e^{x} \end{aligned} \] fill in the blank
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By using the definitions of hyperbolic functions and simplifying, the identity is proven.
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