document.write( "Question 313656: Find all the solutions to the equation. I need help trying to solve the following problem. \r
\n" ); document.write( "\n" ); document.write( "cos(2theta)+2cos^2(theta/2)=2
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Algebra.Com's Answer #224358 by Alan3354(69443)\"\" \"About 
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
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\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
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