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 are also known as the compound angle formulae.


Also see


Sources

  • 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): compound angle formulae (in trigonometry)
  • 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): compound angle formulae (in trigonometry)
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