Formulas

Trig Identities

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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
      \(\tan\alpha \cdot \cot \beta =\) \( \large\frac{{\tan\alpha + \cot \beta }}{{\cot\alpha + \tan \beta }}\normalsize\)