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  4. (1+ tanh (x/2)/1- tanh (x)2) is equal to

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

EAMCETEAMCET 2008

Solution:

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