Q70 / 160 · AP EAMCET 2008 · Mathematics

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

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

Solution

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

Hence, the correct answer is option: 'B'.

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