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

Comments

comments

Posted in: