How to remember the formulas of 和差化積 & 積化和差?
my method:
(1) list the formula of 和角公式
sin(A+B)=sinAcosB + cosAsinB
cos(A+B)=cosAcosB - sinAsinB
I note them as:
s ~ sc +cs
c ~ cc -ss
(2) for 和差化積: let p=(A+B)/2; q=(A-B)/2
then
sinA+sinB=2sinp cosq
sinA-sinB=2cosp sinq
cosA+cosB=2cosp cosq
cosA-cosB=-2sinp sinq
I note them as:
s ~ sc +cs
c ~ cc -ss
(3) for 積化和差: let A=p+q; B=p-q
2sinp cosq=sinA+sinB
2cosp sinq=sinA-sinB
2cosp cosq=cosA+cosB
-2sinp sinq=cosA-cosB
I note them as:
s ~ sc +cs
c ~ cc -ss