Question

求证：sinα+sinβ=2sin(α+β)/2 *cos（α-β）/2

Answer 1

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

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

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

=2cos(a+b)/2sin(a-b)/2