# 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. $Co{s^2}a – Si{n^2}b = Cos(a + b)Cos(a – b) = Co{s^2}b – Si{n^2}a$