Formulas of Sum and Product of Trigonometric Ratios

  1. \[Sina + Sinb = 2Sin\left( {\frac{{a + b}}{2}} \right)Cos\left( {\frac{{a – b}}{2}} \right)\]
  2. \[Sina – Sinb = 2Cos\left( {\frac{{a + b}}{2}} \right)Sin\left( {\frac{{a – b}}{2}} \right)\]
  3. \[Cosa + Cosb = 2Cos\left( {\frac{{a + b}}{2}} \right)Cos\left( {\frac{{a – b}}{2}} \right)\]
  4. \[Cosa – Cosb = – 2Sin\left( {\frac{{a + b}}{2}} \right)Sin\left( {\frac{{a – b}}{2}} \right)\]
  5. \[2{\text{ }}Sina{\text{ }}Cosb = Sin(a + b) + Sin(a – b)\]
  6. \[2{\text{ }}Cosa{\text{ }}Sinb = Sin(a + b) – Sin(a – b)\]
  7. \[2{\text{ }}Cosa{\text{ }}Cosb = Cos(a + b) + Cos(a – b)\]
  8. \[2{\text{ }}Sina{\text{ }}Sinb = Cos(a – b) – Cos(a + b)\]
  9. \[Si{n^2}a – Si{n^2}b = Sin(a + b)Sin(a – b)\]
  10. \[Co{s^2}a – Si{n^2}b = Cos(a + b)Cos(a – b) = Co{s^2}b – Si{n^2}a\]