sina+sinb=2sin((a+b)/2)cos((a-b)/2的推导过程

sina+sinb=2sin((a+b)/2)cos((a-b)/2的推导过程
sina+sinb=2sin((a+b)/2)cos((a-b)/2的推导过程

sina+sinb=2sin((a+b)/2)cos((a-b)/2的推导过程
令a=x+y
b=x-y 则x=(a+b)/2,y=(a-b)/2
sina+sinb=sin(x+y)+sin(x-y)
=sinxcosy+sinycosx+sinxcosy-sinycosx
=2sinxcosy
将 x=(a+b)/2,y=(a-b)/2代入
得sina+sinb=2[sin(a+b)/2][cos(a-b)/2]

sina=sin[(a+b)/2+(a-b)//2]
sinb=sin[(a+b)/2-(a-b)//2]
sina+sinb=2sin[(a+b)/2]cos[(a-b)/2]