Hi
This isn't really a major question or anything its just me trying to cut down on the amount of formulas i need to remember because im very very lazy.
With the Products to Sums and Sums to Products formulae:
2sinAcosB=sin(A+B)+sin(A-B) (1)
2sinBcosA=sin(A+B)-sin(A-B) (2)
2cosAcosB=cos(A+B)+cos(A-B) (3)
-2sinAsinB=cos(A+B)-cos(A-B) (4)
sinS+sinT=2sin((S+T)*1/2)cos((S-T)*1/2) (5)
sinS-sinT=2sin((S+T)*1/2)sin((S-T)*1/2) (6)
cosS+cosT=2cos((S+T)*1/2)cos((S-T)*1/2) (7)
cosS-cosT=-2cos((S+T)*1/2)cos((S-T)*1/2) (
I know that (1) and (3) can be found by the compound angle formula which is pretty easy and I know that (2) is just where A and B has been swapped over so its easy to remember. (5), (6), (7) and (
too are also easy to remember with the corresponding products to sums formula.
Anyway... what I'm asking is if there's a way to derive equation (4) using equations (1) and (3). My teacher told us there was a way but I can't figure it out and I've been trying for a while.
Thank you very much :"D