4.4 Compound Angle Formulas :)

this is a pretty short subtopic :

sin(A + B) DOES NOT equal sinA + sinB. Instead, you must expand such expressions using the formulae below.

The following are important trigonometric relationships:

sin(A + B) = sinAcosB + cosAsinB
cos(A + B) = cosAcosB - sinAsinB
tan(A + B) =   tanA + tanB
                  1 - tanAtanB

To find sin(A - B), cos(A - B) and tan(A - B), just change the + signs in the above identities to - signs and vice-versa:

sin(A - B) = sinAcosB - cosAsinB
cos(A - B) = cosAcosB + sinAsinB
tan(A - B) =   tanA - tanB 
                    1 + tanAtanB