Calculus: Early Transcendentals 8th Edition

cosh(x) + sinh(x) = $e^{x}$
Use the definition of the hyperbolical cosine and sin; the divisor is the same, so it becomes a fraction sum. $$sinh(x) = \frac{e^{x} - e^{-x}}{2}$$ $$cosh(x) = \frac{e^{x} + e^{-x}}{2}$$ $cosh(x) + sinh(x) = \frac{e^{x} - e^{-x}}{2} + \frac{e^{x} + e^{-x}}{2}$ = $\frac{2e^{x}}{2}$ = $e^{x}$