Sin(x+y)cos(x-y)= 1/2sin2x+ 1/2 sin2y

Question

Help please I have no idea how to do this because my math class never did it but while making the final review for the chapter I was assigned, I put this one in it. They are going to all ask me how to do it.

Sin(x+y)cos(x-y)= 1/2sin2x+ 1/2sin2y it says to prove it's an identity. I have literally half a page of work where I do the double angle formulas and try to foil after that but it seems to want me to use the sum and product property to prove it. That's the problem though we never learned it and I can't seem to understand it

Answer 1

so, use the product-to-sum property:

sina cosb = 1/2 (sin(a+b)+sin(a-b))

with a=x+y and b=x-y, that gives

1/2 (sin(2x)+sin(2y))

Not sure why you would have used up so much paper, given that they told you what formula to use...