document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1072633>Question 1072633</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve sin(2x) = sin(x/2) pls. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #687670 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=687670\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sin(2x) = sin(x/2)<BR>\n" );
document.write( " 2sin(x)cos(x) = sin(x/2)<BR>\n" );
document.write( " 2*(2sin(x/2)cos(x/2))*(1 - 2sin^2(x/2)) = sin(x/2)<BR>\n" );
document.write( " Sub t for x/2<BR>\n" );
document.write( " 4sin(t)cos(t) - 8sin^3(t)cos(t) - sin(t) = 0<BR>\n" );
document.write( " --> sin(x/2) = 0 is a root<BR>\n" );
document.write( " --> x = 0<BR>\n" );
document.write( " ===========================<BR>\n" );
document.write( " 4cos(t) -8sin^2(t)cos(t) - 1 = 0\r<BR>\n" );
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document.write( "4cos(t) -8(1-cos^2(t))*cos(t) - 1 = 0\r<BR>\n" );
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document.write( "4cos(t) -8 + 8cos^3(t) - 1 = 0\r<BR>\n" );
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document.write( "8cos^3 + 4cos - 9 = 0<BR>\n" );
document.write( "===========================<BR>\n" );
document.write( "I get roots at 2pi/5 and 6pi/5 graphically, but something's wrong, it doesn't match the calculations.<BR>\n" );
document.write( "I'll work on it later today.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );