$\frac{e^{2 x} - 1}{e^{2 x} + 1}$ in terms of hyperbolic function is

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Solution

$\frac{e^{2 x} - 1}{e^{2 x} + 1}$
Remove $e^{x}$ from both the numerator and denominator.
$= \frac{e^{x} (e^{x} - e^{- x})}{e^{x} (e^{x} + e^{- x})}$
$= \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}}$
$tan h x$ which is a hyperbolic function

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