document.write( "Question 857618: Prove that cos(20°) + cos(100°) + cos(140°) = 0 \n" ); document.write( "
Algebra.Com's Answer #516674 by Edwin McCravy(20065)\"\" \"About 
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document.write( "To prove:  cos(20°) + cos(100°) +cos(140°) = 0\r\n" );
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document.write( "Write the angles in the first two terms in terms \r\n" );
document.write( "of their average, which is 60°, a special angle,\r\n" );
document.write( "and use a double angle identity on each:\r\n" );
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document.write( " cos(20°) = cos(60°-40°) = cos(60°)cos(40°)+sin(60°)sin(40°)\r\n" );
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document.write( "cos(100°) = cos(60°+40°) = cos(60°)cos(40°)-sin(60°)sin(40°)\r\n" );
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document.write( "  SUM OF FIRST TWO TERMS = 2cos(60°)cos(40°) = 2\"%281%2F2%29\"cos(40°) = cos(40°) \r\n" );
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document.write( "Write the angle in the third term in terms of 40° and use\r\n" );
document.write( "use a double angle identity: \r\n" );
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document.write( "cos(140°) = cos(180°-40°) = cos(180°)cos(40°)+sin(180°)sin(40°)\r\n" );
document.write( "                          = (-1)cos(40°) + 0(sin(40°)\r\n" );
document.write( "                          = -cos(40°)\r\n" );
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document.write( "So we have:\r\n" );
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document.write( "cos(20°) + cos(100°) + cos(140°) = cos(40°) - cos(40°) = 0\r\n" );
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document.write( "Edwin
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