Question

$\frac{1+\tanh \frac{x}{2}}{1-\tanh \frac{x}{2}}$ is equal to

• A. $e^{-x}$
• B. $e^x$
• C. $2e^{x/2}$
• D. $2e^{-x/2}$

Answer 1

Answer: (B)

$\frac{1+\tanh \frac{x}{2}}{1-\tanh \frac{x}{2}}$
$=\frac{\cosh \frac{x}{2}+\sinh \frac{x}{2}}{\cosh \frac{x}{2}-\sinh \frac{x}{2}}$
$=\frac{e^{x/2}}{e^{-x/2}}=e^x$