document.write( "Question 1206912: 1. Solve: 3 𝑐os^2𝑥 − 5 cos𝑥 − 2 = 0\r
\n" ); document.write( "\n" ); document.write( "i. 0 ≤ 𝑥 < 2𝜋\r
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\n" ); document.write( "\n" ); document.write( "2. Solve: sin 2𝑥 − 2 cos²𝑥 = 0 over the set of real numbers.\r
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Algebra.Com's Answer #844637 by ikleyn(52817) $\"\"$ $\"About$

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\n" ); document.write( "1. Solve: 3 𝑐os^2𝑥 − 5 cos𝑥 − 2 = 0
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\n" ); document.write( "\n" ); document.write( "2. Solve: sin 2𝑥 − 2 cos²𝑥 = 0 over the set of real numbers.
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document.write( "(1)  3*𝑐os^2(𝑥) − 5*cos𝑥 − 2 = 0.     (1)\r\n" );
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document.write( "     is a quadratic equation relative cos(x).  Use the quadratic formula to find cos(x)\r\n" );
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document.write( "         cos(x) =  =  = .\r\n" );
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document.write( "     The two roots are  cos(x) =  = 2  and  cos(x) =  =  = .\r\n" );
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document.write( "     cos(x) = 2 does not have solution, so we can forget about it.\r\n" );
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document.write( "     cos(x) =  in the interval 0 <= x <   has two solutions\r\n" );
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document.write( "              x =  = 1.9106332  and  x =  -  = 4.3725521 (approximate values).\r\n" );
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document.write( "     Over the set of all real numbers,  equation (1) has two families of solutions\r\n" );
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document.write( "              x =  = 1.9106332 +   and  x =  -  =  - 4.372552064,\r\n" );
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document.write( "                  k = 0, +/-1, +/-2, . . . \r\n" );
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document.write( "(2)  sin 2𝑥 − 2 cos²𝑥 = 0.   (2)\r\n" );
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document.write( "     2*sin(x)*cos(x) - 2*cos^2(x) = 0,\r\n" );
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document.write( "     2*cos(x)*(sin(x) - cos(x)) = 0.\r\n" );
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document.write( "     It deploys in two equations.  First equation is\r\n" );
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document.write( "        cos(x) = 0.\r\n" );
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document.write( "     Over the set of all real numbers, it has solutions  x = ,  k = 0, +/-1, +/-2, . . . \r\n" );
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document.write( "     Second equation is\r\n" );
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document.write( "         sin(x) - cos(x) = 0,  which is equivalent to\r\n" );
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document.write( "         sin(x) = cos(x),  or  tan(x) = 1.\r\n" );
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document.write( "         It has the solutions  x = ,  k = 0, +/-1, +/-2, . . . \r\n" );
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document.write( "      ANSWER.  Over all real numbers, equation (2) has solutions  x =   and/or  x = ,  k = 0, +/-1, +/-2, . . . \r\n" );
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