SOLUTION: if {{{COS(A+B)*SIN(C+D)}}}{{{"="}}}{{{COS(A-B)*SIN(C-D)}}},SHOW THAT {{{COT(A)*COT(B)*COT(C)}}}{{{"="}}}{{{COT(D)}}}

Using well known formulas:



Using "FOIL" on both sides:







(Notice that it took two lines to write that equation because it was so long!
The left side, then the equal sign, then the right side.)

The first terms on each side are the same, so they cancel.
The last terms on each side are also the same so they cancel:







So all we have left is this:



Add the opposites of both negative terms to both sides and we end up with:



Divide both sides by 2



Divide both sides by ,



Cancel what will cancel:





Regroup the factors on the left:



Use the identity  and you end up
with




Edwin