http://www.mapleprimes.com/questions/143058-Question-About-Applyrule en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Sat, 13 Jun 2026 20:45:21 GMT Sat, 13 Jun 2026 20:45:21 GMT The latest answers and comments added to the Question, Question about applyrule http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/questions/143058-Question-About-Applyrule http://www.mapleprimes.com/questions/143058-Question-About-Applyrule?ref=Feed:MaplePrimes:Question about applyrule:Comments#answer143061 <p>Maple does this automatically by &nbsp;<strong>combine &nbsp;</strong>command. But the inverse convertation of the sum to the product - it is a problem:</p> <pre><strong>combine(cos(3*x)*cos(x));</strong><br><strong>combine(cos(3*x)*cos(x) + sin(3*x)*sin(x));</strong></pre> <pre> 1/2*cos(2*x)+1/2*cos(4*x)<br> cos(2*x)</pre> <pre><strong><br></strong></pre> <p>Maple does this automatically by &nbsp;<strong>combine &nbsp;</strong>command. But the inverse convertation of the sum to the product - it is a problem:</p> <pre><strong>combine(cos(3*x)*cos(x));</strong><br><strong>combine(cos(3*x)*cos(x) + sin(3*x)*sin(x));</strong></pre> <pre> 1/2*cos(2*x)+1/2*cos(4*x)<br> cos(2*x)</pre> <pre><strong><br></strong></pre> 143061 Mon, 04 Feb 2013 21:15:00 Z Kitonum Kitonum http://www.mapleprimes.com/questions/143058-Question-About-Applyrule?ref=Feed:MaplePrimes:Question about applyrule:Comments#answer143064 <p>You can apply both those rules, together or separately. Below they are applied separately. Is that what you mean?</p> <pre>restart: ee:=cos(3*x)*cos(x) + sin(3*x)*sin(x): applyrule(cos(a::integer*x)*cos(b::integer*x) =1/2*(cos((a-b)*x)+cos((a+b)*x)), ee); 1 1 - cos(2 x) + - cos(4 x) + sin(3 x) sin(x) 2 2 applyrule(sin(a::integer*x)*sin(b::integer*x) =1/2*(cos((a-b)*x)-cos((a+b)*x)), ee); 1 1 cos(3 x) cos(x) + - cos(2 x) - - cos(4 x) 2 2 </pre> <p>If both are applied, then the terms collapse, and produce just cos(2*x).</p> <!--break--> <p>acer</p> <p>You can apply both those rules, together or separately. Below they are applied separately. Is that what you mean?</p> <pre>restart: ee:=cos(3*x)*cos(x) + sin(3*x)*sin(x): applyrule(cos(a::integer*x)*cos(b::integer*x) =1/2*(cos((a-b)*x)+cos((a+b)*x)), ee); 1 1 - cos(2 x) + - cos(4 x) + sin(3 x) sin(x) 2 2 applyrule(sin(a::integer*x)*sin(b::integer*x) =1/2*(cos((a-b)*x)-cos((a+b)*x)), ee); 1 1 cos(3 x) cos(x) + - cos(2 x) - - cos(4 x) 2 2 </pre> <p>If both are applied, then the terms collapse, and produce just cos(2*x).</p> <!--break--> <p>acer</p> 143064 Mon, 04 Feb 2013 22:43:35 Z acer acer