1. The problem statement, all variables and given/known data I dont understand the example in my book, it says; use the formula for sin(A+B) and sin(A-B) to derive the result that; [itex] sinP + sinQ = 2sin\frac{P+Q}{2} cos\frac{P-Q}{2} [/itex] [itex] sin(A+B) = sinAcosB + cosAcosB [/itex] [itex] sin(A-B) = sinAcosB-cosAsinB [/itex] Add the two intenties to get; [itex] sin(A+B) + sin(A-B) 2sinAcosB [/itex] let A+B = P and A-B=Q then [itex] A = \frac{p+q}{2} [/itex] and [itex] B = \frac{P-Q}{2} [/itex] This is the bit I dont get, How did they get this bit ^^. I understand that the LHS becomes sinP+sinQ but don't understand how they got the fraction? [itex] sinP + sinQ = 2sin\frac{P+Q}{2} cos\frac{P-Q}{2} [/itex]
Hi tweety1234! I'm not sure what you're not getting … you have sin(A+B) + sin(A-B) = 2sinAcosB, and sinAcosB = sin((P+Q)/2)cos((P-Q)/2)
Add the equations A+B = P and A-B=Q, giving 2A = P+Q A = (P+Q)/2. Now subtract those two equations instead of adding them to get B.