How do I write sin(x+y)cos(x-y) as a sum or difference using the product-to-sum formulas?

Question

solomonzelman · Answer

the rules are:

$\large\color{black}{ \displaystyle \sin(a\pm b)=\sin(a)\cos(b)\pm\sin(b)\cos(a)}$

$\large\color{black}{ \displaystyle \cos(a\pm b)=\cos(a)\cos(b)\mp\sin(a)\sin(b)}$

a1234 · Answer

I did those and came up with (sinx cosy + cosx siny) (cosx cosy + sinx siny)

solomonzelman · Answer

Ok, very good!

a1234 · Answer

But the choices I have are:

A. 1/2(sin2x + sin2y)
B. -1/2(sin2x + sin2y)
C. 2sinxsiny
D. -2sinxsiny

a1234 · Answer

@SolomonZelman

solomonzelman · Answer

expand it and try to re-write it.
What you had is correct, but in different form.