Formulas and Tables

Trigonometry

Product-to-Sum Identities

Angles (arguments of functions): \(\alpha\), \(\beta\)

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

  1. Product of sines
    \(\sin \alpha \cdot \sin \beta =\) \( \large\frac{{\cos \left( {\alpha – \beta } \right) – \cos \left( {\alpha + \beta } \right)}}{2}\normalsize\)
  2. Product of cosines
    \(\cos \alpha \cdot \cos \beta =\) \( \large\frac{{\cos \left( {\alpha – \beta } \right) + \cos \left( {\alpha + \beta } \right)}}{2}\normalsize\)
  3. Product of sine and cosine
    \(\sin \alpha \cdot \cos \beta =\) \( \large\frac{{\sin \left( {\alpha – \beta } \right) + \sin \left( {\alpha + \beta } \right)}}{2}\normalsize\)
  4. Product of tangents
    \(\tan\alpha \cdot \tan \beta =\) \( \large\frac{{\tan\alpha + \tan \beta }}{{\cot\alpha + \cot \beta }}\normalsize\)
  5. Product of cotangents
    \(\cot\alpha \cdot \cot \beta =\) \( \large\frac{{\cot\alpha + \cot \beta }}{{\tan\alpha + \tan \beta }}\normalsize\)
  6. Product of tangent and cotangent
    \(\tan\alpha \cdot \cot \beta =\) \( \large\frac{{\tan\alpha + \cot \beta }}{{\cot\alpha + \tan \beta }}\normalsize\)