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 Trigonometric Subtraction Formulas 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

• Addition Formulas

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

Sources

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