Calculus: Early Transcendentals 8th Edition

cosh(x) - sinh(x) = $e^{-x}$
Use the definition of the hyperbolical sine and cosine and do a simple fraction subtraction. $$sinh(x) = \frac{e^{x} - e^{-x}}{2}$$ $$cosh(x) = \frac{e^{x} + e^{-x}}{2}$$ cosh(x) - sinh(x) = $\frac{e^{x} + e^{-x}}{2}$ - $\frac{e^{x} - e^{-x}}{2}$ = $\frac{2e^{-x}}{2}$ = $e^{-x}$