Sum difference product
2 sinA cosB = sin(A+B)+sin(A-B)2 cosA sinB = sin(A+B)-sin(A-B)2 cosA cosB = cos(A+B)-sin(A-B)-2 sinA sinB = cos(A+B)-cos(A-B)sinA+sinB = 2 sin((A+B)/ 2 cos((A-B)/2 cosA+cosB = 2 cos((A+B)/2)sin((A-B)/2)tanA+tanB = sin(A+B)/cosA cosB = sin(A+B)
Auxiliary angle formula
asina+bcosa=(a2+b2)^( 1/2)sin(a+t)
asina-bcosa=(a2+b2)^( 1/2)cos(a-t)