Question

$\frac{1+\tanh \frac{x}{2}}{1-\tanh \frac{x}{2}}$ =

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

Answer 1

Answer: (B)

$e^x$

Let $f\left(x\right)=\frac{1+\tan \frac{hx}{2}}{1-\tan \frac{hx}{2}}=\frac{\sin \frac{hx}{2}+\cos \frac{hx}{2}}{\cos \frac{hx}{2}-\sin \frac{hx}{2}}$
$=\frac{e^{\frac{x}{2}}}{+e^{-\frac{x}{2}}}$
$=e^x$