Question 1028367
<pre>
Add the two equations:

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

Get
{{{cos(A+B)+cos(A-B)=2cos(A)cos(B)}}}

Multiply both sides by 1/2

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

Swap sides:

{{{cos(A)cos(B)=expr(1/2)(cos(A+B)+cos(A-B)^"")}}} <--product-to-sum formula

Let {{{A=6theta}}}, {{{B=2theta}}}

{{{cos(6theta)cos(2theta)=expr(1/2)(cos(6theta+2theta)^""+cos(6theta-2theta))}}}

{{{cos(6theta)cos(2theta)=expr(1/2)(cos(8theta)^""+cos(4theta))}}}

Edwin</pre>