Question

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

Answer 1

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]