Double Angle Formulas

Theorem

Double Angle Formula for Sine

$\sin 2 \theta = 2 \sin \theta \cos \theta$

Double Angle Formula for Cosine

$\cos 2 \theta = \cos^2 \theta - \sin^2 \theta$

Double Angle Formula for Tangent

$\tan 2 \theta = \dfrac {2 \tan \theta} {1 - \tan^2 \theta}$

where $\sin, \cos, \tan$ denote sine, cosine and tangent respectively.

Hyperbolic Functions

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.

Also see

• Triple Angle Formulas

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): double-angle formula
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): double-angle formulae
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): double-angle formulae
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): double-angle formula (in trigonometry)