document.write( "Question 921917: Solve for x: cos(4x)-(1/2)sin(4x)=1 \n" ); document.write( "

Algebra.Com's Answer #559281 by lwsshak3(11628) $\"\"$ $\"About$

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Solve for x: cos(4x)-(1/2)sin(4x)=1, For[0,90˚]
\n" ); document.write( "let u=4x
\n" ); document.write( "cosu-sinu/2=1
\n" ); document.write( "2cosu-sinu=2
\n" ); document.write( "2cosu-2=sinu
\n" ); document.write( "2(cosu-1)=sinu
\n" ); document.write( "square both sides
\n" ); document.write( "4(cos^2u-2cosu+1)=sin^2u
\n" ); document.write( "4cos^2u-8cosu+4=1-cos^2u
\n" ); document.write( "5cos^2u-8cosu+3=0
\n" ); document.write( "(cosu-1)(5cosu-3)=0
\n" ); document.write( "cosu=1
\n" ); document.write( "u=0=4x
\n" ); document.write( "x=0
\n" ); document.write( "or
\n" ); document.write( "cosu=3/5
\n" ); document.write( "u≈53.13˚=4x
\n" ); document.write( "x≈13.28˚
\n" ); document.write( " \n" ); document.write( "

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