Formulas and Tables

Trigonometry

Addition and Subtraction Formulas

Angles: \(\alpha\), \(\beta\)

Trigonometric functions: \(\sin \alpha,\) \(\cos \alpha,\) \(\tan \alpha,\) \(\cot \alpha\)

  1. Sine addition formula
    \(\sin \left( {\alpha + \beta } \right) =\) \( \sin \alpha \cos \beta \,+\) \( \cos \alpha \sin \beta \)
  2. Sine subtraction formula
    \(\sin \left( {\alpha – \beta } \right) =\) \( \sin \alpha \cos \beta \,-\) \( \cos \alpha \sin \beta \)
  3. Cosine addition formula
    \(\cos \left( {\alpha + \beta } \right) =\) \( \cos \alpha \cos \beta \,-\) \( \sin \alpha \sin \beta \)
  4. Cosine subtraction formula
    \(\cos \left( {\alpha – \beta } \right) =\) \( \cos \alpha \cos \beta \,+\) \( \sin \alpha \sin \beta \)
  5. Tangent addition formula
    \(\tan \left( {\alpha + \beta } \right) = \large\frac{{\tan \alpha + \tan \beta }}{{1 – \tan \alpha \tan \beta }}\normalsize\)
  6. Tangent subtraction formula
    \(\tan \left( {\alpha – \beta } \right) = \large\frac{{\tan \alpha – \tan \beta }}{{1 + \tan \alpha \tan \beta }}\normalsize\)
  7. Cotangent addition formula
    \(\cot \left( {\alpha + \beta } \right) = \large\frac{{1 – \tan \alpha \tan \beta }}{{\tan \alpha + \tan \beta }}\normalsize\)
  8. Cotangent subtraction formula
    \(\cot \left( {\alpha – \beta } \right) = \large\frac{{1 + \tan \alpha \tan \beta }}{{\tan \alpha – \tan \beta }}\normalsize\)