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document.write( "1 + cos(6x) - 2cos(4x) = 0\r\n" );
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document.write( "The idea of solution is to express cos(6x) via cos(2x) and express cos(4x) via cos(2x) to get in this way\r\n" );
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document.write( "an equation for cos(2x) uniformly in the left side.\r\n" );
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document.write( "For it, use widely known formulas of Trigonometry\r\n" );
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document.write( " cos(3a) = 
, (1) and\r\n" );
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document.write( " cos(2a) = 
. (2)\r\n" );
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document.write( "Use a = 2x; then formulas (1) and (2) give you\r\n" );
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document.write( " cos(6x) = 
, (3) and\r\n" );
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document.write( " cos(4x) = 
. (4)\r\n" );
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document.write( "Now substitute (3) and (4) into your basic equation. You will get\r\n" );
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document.write( " 
= 0, or\r\n" );
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document.write( " 
= 0. (5)\r\n" );
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document.write( "In the last equation, introduce new variable y = cos(2x). You will get then\r\n" );
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document.write( " 
= 0.\r\n" );
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document.write( "You can group the terms and factor it in this way\r\n" );
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document.write( " 
= 0,\r\n" );
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document.write( " 
= 0.\r\n" );
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document.write( "So the roots for y are 
= 1; 
= 
and 
= -.\r\n" );
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document.write( "Thus we have three cases to analyse separately:\r\n" );
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document.write( " Case 1. = 1 ====> cos(2x) = 1 ====> 2x = 0 or 
====> x = 0 or x = 
. \r\n" );
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document.write( " Case 2. = ====> cos(2x) = ====> 2x = 
or 2x = 
====> x = 
or x = 
. \r\n" );
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document.write( " Case 3. = - ====> cos(2x) = - ====> 2x = 
or 2x = 
====> x = 
or x = 
. \r\n" );
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document.write( "ANSWER. In all, there are 6 solutions for x in the given interval:\r\n" );
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document.write( " x = 0; ; ; ; and .\r\n" );
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document.write( "Solved.\r
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