document.write( "Question 1162905: Express the function below as a sum or difference of sine and cosine.
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Algebra.Com's Answer #786823 by Edwin McCravy(20060) $\"\"$ $\"About$

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sin4xcos3x
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document.write( "This looks like part of the right side of the formulas for sin(A + B) and\r\n" );
document.write( "sin(A - B), which are:\r\n" );
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document.write( "               sin(A + B) = sin(A)cos(B) + cos(A)sin(B)\r\n" );
document.write( "               sin(A - B) = sin(A)cos(B) - cos(A)sin(B)\r\n" );
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document.write( "So we write them both substituting A = 4x and B = 3x\r\n" );
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document.write( "               sin(4x + 3x) = sin(4x)cos(3x) + cos(4x)sin(3x)\r\n" );
document.write( "               sin(4x - 3x) = sin(4x)cos(3x) - cos(4x)sin(3x)\r\n" );
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document.write( "Simplifying the left sides:\r\n" );
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document.write( "               sin(7x) = sin(4x)cos(3x) + cos(4x)sin(3x)\r\n" );
document.write( "                sin(x) = sin(4x)cos(3x) - cos(4x)sin(3x)\r\n" );
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document.write( "Next we add those equations together vertically, term by term,\r\n" );
document.write( "we see that the last terms on the right cancel out:\r\n" );
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document.write( "      sin(7x) + sin(x) = 2sin(4x)cos(3x)\r\n" );
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document.write( "We multiply both sides by 1/2 and the right side will become\r\n" );
document.write( "what was given:\r\n" );
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document.write( "So the left side is the answer since the right side is what was given\r\n" );
document.write( "and the left side is a sum.\r\n" );
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document.write( "Edwin

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