document.write( "Question 1183076: Find the solutions of the equation cos 2x + cos 𝑥 + 1 = 0 in the interval [0, 2𝜋). \n" ); document.write( "

Algebra.Com's Answer #813233 by ikleyn(52814) $\"\"$ $\"About$

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\n" ); document.write( "Find the solutions of the equation cos 2x + cos 𝑥 + 1 = 0 in the interval [0, 2𝜋).
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document.write( "Your starting equation is\r\n" );
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document.write( "    cos(2x) + cos 𝑥 + 1 = 0    (1)\r\n" );
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document.write( "Use  cos(2x) = 2cos^2(x) - 1.   Substitute it into the given equation.  You will get\r\n" );
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document.write( "    (2cos^2(x) - 1) + cos(x) + 1 = 0,   or\r\n" );
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document.write( "     2cos^2(x) + cos(x) = 0.\r\n" );
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document.write( "Factor left side\r\n" );
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document.write( "    (2cos(x) + 1)*cos(x) = 0.\r\n" );
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document.write( "So,  EITHER  cos(x) = 0, giving  x = ,  ,\r\n" );
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document.write( "     OR      2cos(x) + 1 = 0,  giving  cos(x) = - ,   x = ,  .\r\n" );
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document.write( "ANSWER.  The solutions are  ,  ,  ,  .\r\n" );
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