document.write( "Question 770556: Rewrite as a sum, then simplify if possible: cos3xsin11x \n" ); document.write( "
Algebra.Com's Answer #469620 by Edwin McCravy(20060)\"\" \"About 
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document.write( "cos(3x)sin(11x)\r\n" );
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document.write( "That's a product of a cosine and a sine.  Usually sines\r\n" );
document.write( "come before cosines, so let's reverse the two factors:\r\n" );
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document.write( "Let's rewrite it as\r\n" );
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document.write( "sin(11x)cos(3x)\r\n" );
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document.write( "We think through the formulas for AħB\r\n" );
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document.write( "sin(AħB) = sin(A)cos(B) ħ cos(A)sin(B)\r\n" );
document.write( "cos(AħB) = cos(A)cos(B) ∓ sin(A)sin(B)\r\n" );
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document.write( "and see that the first formula contains such a product, \r\n" );
document.write( "sin(A)cos(B),\r\n" );
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document.write( "so we let A=11x and B=3x, then \r\n" );
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document.write( "sin(AħB) = sin(A)cos(B) ħ cos(A)sin(B)\r\n" );
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document.write( "becomes the two equations:\r\n" );
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document.write( "sin(11x+3x) = sin(11x)cos(3x) + cos(11x)sin(3x)\r\n" );
document.write( "sin(11x-3x) = sin(11x)cos(3x) - cos(11x)sin(3x)\r\n" );
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document.write( "or\r\n" );
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document.write( "sin(14x) = sin(11x)cos(3x) + cos(11x)sin(3x)\r\n" );
document.write( " sin(8x) = sin(11x)cos(3x) - cos(11x)sin(3x)\r\n" );
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document.write( "Addinng those equations term by term:\r\n" );
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document.write( "sin(14x) + sin(8x) = 2sin(11x)cos(3x)\r\n" );
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document.write( "Solving for sin(11x)cos(3x) by multiplying both sides by \"1%2F2\"\r\n" );
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document.write( "\"1%2F2\"[sin(14x) + sin(8x)] = sin(11x)cos(3x)\r\n" );
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document.write( "\"1%2F2\"sin(14x) + \"1%2F2\"sin(8x)] = sin(11x)cos(3x)\r\n" );
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document.write( "Edwin
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