document.write( "Question 544641: Find the exact solutions in the interval [ 0 , 2π] for cos 2x – cos x = 0. \n" ); document.write( "

Algebra.Com's Answer #355516 by lwsshak3(11628) $\"\"$ $\"About$

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Find the exact solutions in the interval [ 0 , 2π] for cos 2x – cos x = 0
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\n" ); document.write( "cos2x – cosx = 0
\n" ); document.write( "Identity: cos 2x=2cos^2x-1
\n" ); document.write( "2cos^2x-1 – cosx = 0
\n" ); document.write( "2cos^2x– cosx-1 = 0
\n" ); document.write( "(2cosx+1)(cosx-1)=0
\n" ); document.write( "..
\n" ); document.write( "2cosx+1=0
\n" ); document.write( "cosx=-1/2
\n" ); document.write( "x=2π/3 and 4π/3 (in quadrants II and III where cos<0
\n" ); document.write( "..
\n" ); document.write( "cosx-1=0
\n" ); document.write( "cosx=1
\n" ); document.write( "x=0
\n" ); document.write( "..
\n" ); document.write( "ans:
\n" ); document.write( "Exact solutions in the interval [ 0 , 2π]
\n" ); document.write( "x=0, 2π/3 and 4π/3 \n" ); document.write( "

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