document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178162>Question 1178162</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation for exact solutions in the interval 0 ≤ x < 2𝜋.\r<BR>\n" );
document.write( "\n" );
document.write( "sin 4x − sqrt3 sin 2x = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #807364 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=807364\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%284x%29-sqrt%283%29%2Asin%282x%29=0 ALIGN=MIDDLE  ALT=\"sin%284x%29-sqrt%283%29%2Asin%282x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The arguments for sine are 4x and 2x.  Use the double angle formula for sine to represent sin(4x) in terms of sin(2x) and cos(2x).<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sin%282x%29cos%282x%29-sqrt%283%29%2Asin%282x%29=0 ALIGN=MIDDLE  ALT=\"2sin%282x%29cos%282x%29-sqrt%283%29%2Asin%282x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Factor (the terms have a common factor of sin(2x))<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282x%29%282cos%282x%29-sqrt%283%29%29=0 ALIGN=MIDDLE  ALT=\"sin%282x%29%282cos%282x%29-sqrt%283%29%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282x%29=0 ALIGN=MIDDLE  ALT=\"sin%282x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2cos%282x%29-sqrt%283%29=0 ALIGN=MIDDLE  ALT=\"2cos%282x%29-sqrt%283%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "I'll leave it for you to finish from there.<br><BR>\n" );
document.write( "Re-post, showing the work you have done, if you need more help.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );