Answer: I dont have one for sure but I can explain why this is true.
Step by Step:
sin(x+y)−sin(x−y)=sinxcosy+sinycosx−(sinxcosy−sinycosx)
=sinxcosy+sinycosx−sinxcosy+sinycosx
=sinxcosy+sinycosx−sinxcosy+sinycosx
=sinycosx+sinycosx
=2sinycosx
henceforth proved.
