document.write( "Question 1155029: Find all solutions of each equation in the interval [0,2π)\r
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Algebra.Com's Answer #777589 by ikleyn(52835) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "The general statement is \r\n" );
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document.write( "    If cos(a) + cos(b) = 0, then\r\n" );
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document.write( "        EITHER  a + b =  + \r\n" );
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document.write( "        OR      a - b =  + .\r\n" );
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document.write( "If apply it to  x  and  3x,  then\r\n" );
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document.write( "    EITHER  x + 3x =  + \r\n" );
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document.write( "    OR      |x - 3x| =  + .\r\n" );
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document.write( "First case gives\r\n" );
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document.write( "    4x = ;  hence,  x = ,  or  x = ,  or  x = ,  or  x = .\r\n" );
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document.write( "Second case gives\r\n" );
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document.write( "   2x = ;  hence,  x = ,  or  x = .\r\n" );
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document.write( "These 6 listed values are the full set of solutions to the given equation in given interval.\r\n" );
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document.write( "Use the general formula\r\n" );
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document.write( "    cos(a) + cos(b) = .\r\n" );
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document.write( "When you apply it with  x  and  3x, you get\r\n" );
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document.write( "    cos(x) + cos(3x) = 2*cos(2x)*cos(x) = 0,\r\n" );
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document.write( "which leads you to the SAME answer.\r\n" );
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