Compound Angle Formulas

Trigonometric Addition Formulas

Sine of Sum

$\map \sin {a + b} = \sin a \cos b + \cos a \sin b$

Cosine of Sum

$\map \cos {a + b} = \cos a \cos b - \sin a \sin b$

Tangent of Sum

$\map \tan {a + b} = \dfrac {\tan a + \tan b} {1 - \tan a \tan b}$

Trigonometric Subtraction Formulas

Sine of Difference

$\map \sin {a - b} = \sin a \cos b - \cos a \sin b$

Cosine of Difference

$\map \cos {a - b} = \cos a \cos b + \sin a \sin b$

Tangent of Difference

$\map \tan {a - b} = \dfrac {\tan a - \tan b} {1 + \tan a \tan b}$

Also known as

The Compound Angle Formulas are also known as the Compound Angle Formulae.

Also see

• Addition Formulas for Hyperbolic Functions
• Subtraction Formulas for Hyperbolic Functions

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): compound angle formulae (in trigonometry)