Hyperbolic Functions 2 (AQA A-Level Further Maths): Flashcards

$\sinh x = \frac{1}{2}(e^x - e^{-x})$

$\cosh x = \frac{1}{2}(e^x + e^{-x})$

$\tanh x = \frac{e^x - e^{-x}}{e^x + e^{-x}}$

$\ln(x + \sqrt{x^2 + 1})$

$\ln(x + \sqrt{x^2 - 1})$ for $x \geq 1$

$\frac{1}{2}\ln\left(\frac{1+x}{1-x}\right)$, $-1 < x < 1$

$\cosh^2 x - \sinh^2 x \equiv 1$

$1 - \tanh^2 x \equiv \text{sech}^2 x$

$\sinh 2x \equiv 2\sinh x \cosh x$

$\cosh 2x \equiv \cosh^2 x + \sinh^2 x$