Trigonometric Subtraction Formulas

Theorem

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 trigonometric subtraction formulae.

They are also known just as the subtraction formulas or subtraction formulae.

They are often seen categorised along with the trigonometric addition formulas as the compound angle formulas.


Also see


Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): addition formulae
  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): subtraction formulae
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): addition formulae
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): subtraction formulae
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