Answer
$e^{x}$ = 5
sinh x = $\frac{12}{5}$
cosh x = $\frac{13}{5}$
Work Step by Step
We know that
$\frac{1 + tanh x}{1 - tanh x}$ = $e^{2x}$
Substitute tanh x = $\frac{12}{13}$ , To get
$\frac{1 + \frac{12}{13}}{1 - \frac{12}{13}}$ = $e^{2x}$
$\frac{13 + 12}{13 - 12}$ = $e^{2x}$
25 = $e^{2x}$
$e^{x}$ = 5
Thus, we know:
sinh = $\frac{e^{x}-e^{-x}}{2}$ = $\frac{5 - \frac{1}{5}}{2}$ = $\frac{\frac{25}{5}-\frac{1}{5}}{2}$ = $\frac{12}{5}$
cosh x = $\frac{e^{x} + e^{-x}}{2}$ = $\frac{5 + \frac{1}{5}}{2}$ = $\frac{\frac{25}{5} + \frac{1}{5}}{2}$ = $\frac{13}{5}$
