document.write( "Question 313656: Find all the solutions to the equation. I need help trying to solve the following problem. \r
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document.write( "cos(2theta)+2cos^2(theta/2)=2 \n" );
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Algebra.Com's Answer #224358 by Alan3354(69443)![]() ![]() You can put this solution on YOUR website! cos(2theta)+2cos^2(theta/2)=2 \n" ); document.write( "I'll use x, less typing \n" ); document.write( "cos(2x)+2cos^2(x/2)=2 \n" ); document.write( "cos(2x) = 2cos^2(x) - 1 \n" ); document.write( "------------------------ \n" ); document.write( "2cos^2(x) - 1 + 2cos^2(x/2) = 2 \n" ); document.write( "2cos^2(x) + 2cos^2(x/2) = 3 \n" ); document.write( "y = x/2 \n" ); document.write( "2cos^2(2y) + 2cos^2(y) = 3 \n" ); document.write( "2(2cos^2(y) - 1)^2 + 2cos^2(y) = 3 \n" ); document.write( "8cos^4(y) - 8cos^2(y) + 2 + 2cos^2(y) = 3 \n" ); document.write( "8cos^4(y) - 6cos^2(y) - 1 = 0 \n" ); document.write( "A quadratic in cos^2(y) \n" ); document.write( "cos^2(y) = 3/8 ± sqrt(17)/8 =~ 0.890388 \n" ); document.write( "cos(y) =~ 0.9436038 \n" ); document.write( "y =~ ± 19.334º \n" ); document.write( "theta =~ ± 38.668º (principal value)\r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |