Question 1070185
<pre>
Adding the formulas

{{{system(sin(A+B)=sin(A)cos(B)+cos(A)sin(B),sin(A-B)=sin(A)cos(B)-cos(A)sin(B))}}}

we get

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

or 

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

or the product-to-sum formula:

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

Substituting A = 4d, B = d

{{{sin(4d)cos(d)}}}{{{""=""}}}{{{expr(1/2)(sin(4d+d)+sin(4d-d)^"")}}}{{{""=""}}}{{{expr(1/2)(sin(5d)+sin(3d)^"")}}}

Edwin</pre>