document.write( "Question 515587: Please help me with this problem,\r
\n" ); document.write( "\n" ); document.write( "express sin(3x)cos(5x) as a sum or difference of trig functions.\r
\n" ); document.write( "\n" ); document.write( "Thank You \n" ); document.write( "
Algebra.Com's Answer #344082 by drcole(72)\"\" \"About 
You can put this solution on YOUR website!
Let's recall the sum and difference formulae for the sine function:\r
\n" ); document.write( "\n" ); document.write( "\"sin%28alpha+%2B+beta%29+=+sin%28alpha%29+cos%28beta%29+%2B+cos%28alpha%29+sin%28beta%29+\"
\n" ); document.write( "\"sin%28alpha+-+beta%29+=+sin%28alpha%29+cos%28beta%29+-+cos%28alpha%29+sin%28beta%29+\"\r
\n" ); document.write( "\n" ); document.write( "If we sum these two equations (in other words, add together the left hand sides and the right hand sides), the term with \"cos%28alpha%29+sin%28beta%29\" will cancel out, leaving:\r
\n" ); document.write( "\n" ); document.write( "\"sin%28alpha+%2B+beta%29+%2B+sin%28alpha+-+beta%29+=+2+sin%28alpha%29+cos%28beta%29+\"
\n" ); document.write( " (dividing both sides by 2)\r
\n" ); document.write( "\n" ); document.write( "So . In your problem, \"alpha+=+3x\" and \"beta+=+5x\", so we get:\r
\n" ); document.write( "\n" ); document.write( "\"sin%283x%29+cos%285x%29+=+%281%2F2%29+%2A+%28sin%283x+%2B+5x%29+%2B+sin%283x+-+5x%29%29+\"
\n" ); document.write( "\"+sin%283x%29+cos%285x%29+=+%281%2F2%29+%2A+%28sin%288x%29+%2B+sin%28-2x%29%29+\" (simplifying)
\n" ); document.write( "\"+sin%283x%29+cos%285x%29+=+%281%2F2%29+%2A+%28sin%288x%29+-+sin%282x%29%29+\" (recalling that for any \"theta\", \"sin%28-theta%29+=+-sin%28theta%29\")
\n" ); document.write( "\"+sin%283x%29+cos%285x%29+=+%281%2F2%29+%2A+sin%288x%29+-+%281%2F2%29+%2A+sin%282x%29+\" (distributing the \"1%2F2\")
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