Question

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

Answer 1

the rules are:

\(\large\color{black}{ \displaystyle \sin(a\pm b)=\sin(a)\cos(b)\pm\sin(b)\cos(a)}\)

\(\large\color{black}{ \displaystyle \cos(a\pm b)=\cos(a)\cos(b)\mp\sin(a)\sin(b)}\)

Answer 2

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

Answer 3

Ok, very good!

Answer 4

But the choices I have are:

A. 1/2(sin2x + sin2y)
B. -1/2(sin2x + sin2y)
C. 2sinxsiny
D. -2sinxsiny

Answer 5

@SolomonZelman

Answer 6

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