Question

证明(sin x-sin y)/sin (x+y)=sin[(x-y)/2]/sin[(x+y)/2]

Answer 1

证明：(sinx-siny)/sin(x+y)={2cos[(x+y)/2]*sin[(x-y)/2]}/{2sin[(x+y)/2]*cos[(x+y)/2]}

(直接应用正弦和差化积公式和正弦半角公式)

=sin[(x-y)/2]/cos[(x+y)/2].