document.write( "Question 1126751: What is the value of cos(2α) , if 2 cos(3α)= cos(α)? \n" ); document.write( "

Algebra.Com's Answer #743075 by ikleyn(52790) $\"\"$ $\"About$

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document.write( "Start from this basic identity\r\n" );
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document.write( "    cos(3a)=4*cos^3(a) - 3*cos(a).\r\n" );
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document.write( "Then 2*cos(3a) = 8*cos^3(a) - 6*cos(a),  and we are given that\r\n" );
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document.write( "    8*cos^3(a) - 6*cos(a) = cos(a).\r\n" );
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document.write( "It implies\r\n" );
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document.write( "     = 0.\r\n" );
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document.write( "So, either  cos(a) = 0   or    = 0;  the last is equivalent to   = .\r\n" );
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document.write( "Case 1.  If  cos(a) = 0,  then  cos(2a) =  = -1.\r\n" );
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document.write( "Case 2.  If   = ,  then  cos(2a) =  =  =  =  = .\r\n" );
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document.write( "Answer.  If  2*cos(3a) = cos(a),  then EITHER  cos(2a) = -1  OR  cos(2a) = .\r\n" );
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