Double Angle Formulas/Hyperbolic Functions

Theorem

Double Angle Formula for Hyperbolic Sine

$\sinh 2 x = 2 \sinh x \cosh x$


Double Angle Formula for Hyperbolic Cosine

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


Double Angle Formula for Hyperbolic Tangent

$\tanh 2 x = \dfrac {2 \tanh x} {1 + \tanh^2 x}$


where $\sinh, \cosh, \tanh$ denote hyperbolic sine, hyperbolic cosine and hyperbolic tangent respectively.


Also known as

Some sources hyphenate: double-angle formulas.


Sources

  • 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): double-angle formula (in hyperbolic functions)
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