Question 1099317
<pre>
I tried it using the identity that you chose, but it became
more and more complicated, so I tried the "product to sum"
formula above, and, as you see, it was fairly straight forward.  
I could also have used the "sum to product" formula working 
with the right side.  The formulas you need for such problems are:

Sum or difference to product:

{{{sin(A)+sin(B)}}}{{{""=""}}}{{{2sin(expr(1/2)(A+B))cos(expr(1/2)(A-B))}}}

{{{sin(A)-sin(B)}}}{{{""=""}}}{{{2sin(expr(1/2)(A-B))cos(expr(1/2)(A+B))}}}

{{{cos(A)+cos(B)}}}{{{""=""}}}{{{2cos(expr(1/2)(A+B))cos(expr(1/2)(A-B))}}}

{{{cos(A)-cos(B)}}}{{{""=""}}}{{{-2sin(expr(1/2)(A+B))sin(expr(1/2)(A-B))}}}

Product to sum or difference

{{{sin(A)cos(B)}}}{{{""=""}}}{{{expr(1/2)(sin(A+B)+sin(A-B)^"")}}}

{{{cos(A)cos(B)}}}{{{""=""}}}{{{expr(1/2)(cos(A+B)+cos(A-B)^"")}}}

{{{sin(A)sin(B)}}}{{{""=""}}}{{{expr(1/2)(cos(A-B)-cos(A+B)^"")}}}
 
All those are easily proved using formulas for sin(AħB) and cos(AħB)

Edwin</pre>(AKA AnlytcPhil)