Question

The value of $\dfrac{1 + \tanh x}{1 - \tanh x} =$ ?

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

Hint:

Use $\tanh x = \frac{e^x - e^{-x}}{e^x + e^{-x}}$ to simplify complex hyperbolic expressions.

Answer 1

The Correct Option is C

Use the identity: \[ \tanh x = \frac{e^x - e^{-x}}{e^x + e^{-x}} \Rightarrow \frac{1 + \tanh x}{1 - \tanh x} = \frac{e^{2x} + 1 + e^{2x} - 1}{e^{2x} + 1 - (e^{2x} - 1)} = \frac{2e^{2x}}{2} = e^{2x} \]