sinA+sinB=2sin((A+B)/2)cos((A-B)/2的推导过程是怎样的?

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]