 Quandaries and Queries Who is asking: Student Level: Secondary Question: Prove: sin A + sin B = 2sin(A+B/2)cos(A-B/2) cos A - cos B = -2sin(A+B/2)sin(A-B/2) cos A + cos B = 2cos(A+B/2)cos(A-B/2) sin A - sin B = 2cos(A+B/2)sin(A+B/2) Please help im almost there with these babies and it's very frustrating! Hi, I will illustrate how to derive the first expression. To do it I am going to assume that you know that sin(P + Q) = sin(P)cos(Q) + cos(P)sin(Q) (equation 1) and that sin(-P) = -sin(P) and cos(-P) = cos(P) From these I can derive sin(P - Q) = sin(P + (- Q)) = sin(P)cos(-Q) + cos(P)sin(-Q) so sin(P - Q) = sin(P)cos(Q) - cos(P)sin(Q) (equation 2) Adding equation 1 and equation 2 I get sin(P + Q) + sin(P - Q) = sin(P)cos(Q) + cos(P)sin(Q) + sin(P)cos(Q) - cos(P)sin(Q) thus sin(P + Q) + sin(P - Q) = 2 sin(P)cos(Q) If you now let P = A + B/2 and Q = A - B/2 you will se that this is exactly the expression in your first problem. The other can be derived in a similar fashion. Penny Go to Math Central