document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062122>Question 1062122</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Good morning, can somebody help me factorize and solve step by step following equation?:<BR>\n" );
document.write( "sin(2x)cos(pi/3) - cos(2x)sin(pi/3) + 3^(1/2)(cos(2x)cos(pi/3) + sin(2x)sin(pi/3))-3^(1/2) = 0<BR>\n" );
document.write( "Thank you very much RB </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #676931 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=676931\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> -sqrt(3) - 1/2 sqrt(3) cos(2 x) + 1/2 sin(2 x) + sqrt(3) (1/2 cos(2 x) + 1/2 sqrt(3) sin(2 x)) = 0<BR>\n" );
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document.write( "Simplify and substitute y = 1/2 sin(2 x)<BR>\n" );
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document.write( "-sqrt(3) - 1/2 sqrt(3) cos(2 x) + 1/2 sin(2 x) + sqrt(3) (1/2 cos(2 x) + 1/2 sqrt(3) sin(2 x)) = (4 sin(2 x))/2 - sqrt(3) = 4y - sqrt(3) = 0<BR>\n" );
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document.write( "4y - sqrt(3) = 0<BR>\n" );
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document.write( "Add sqrt(3) to both sides<BR>\n" );
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document.write( "4y = sqrt(3)<BR>\n" );
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document.write( "Divide both sides by 4<BR>\n" );
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document.write( "y = sqrt(3)/4<BR>\n" );
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document.write( "Substitute back for y = 1/2 sin(2 x)<BR>\n" );
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document.write( "1/2 sin(2x) = sqrt(3)/4<BR>\n" );
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document.write( "Multiply both sides by 2<BR>\n" );
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document.write( "sin(2x) = sqrt(3)/2<BR>\n" );
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document.write( "Take the inverse sine of both sides<BR>\n" );
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document.write( "2x = (2&#960;)/3 + 2&#960;n1 for n1 in Z<BR>\n" );
document.write( "or 2x = &#960;/3 + 2&#960;n2 for n2 in Z<BR>\n" );
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document.write( "Simplify each equation<BR>\n" );
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document.write( "Divide both sides by 2<BR>\n" );
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document.write( "x = &#960;/3 + &#960;n1 for n1 in Z<BR>\n" );
document.write( "or 2x = &#960;/3 + 2&#960;n2 for n2 in Z<BR>\n" );
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document.write( "Divide both sides by 2<BR>\n" );
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document.write( "x = &#960;/3 + &#960;n1 for n1 in Z<BR>\n" );
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document.write( "or x = &#960;/6 + &#960;n2 for n2 in Z<BR>\n" );
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