document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=522871>Question 522871</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve sin(5x)cos(8x)-cos(5x)sin(8x)=-0.5  for the smallest positive solution.\r<BR>\n" );
document.write( "\n" );
document.write( "x= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #347133 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=347133\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> solve sin(5x)cos(8x)-cos(5x)sin(8x)=-0.5 for the smallest positive solution. <BR>\n" );
document.write( "x=<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Identity: sin(s-t)=sin s cos t-cos s sin t<BR>\n" );
document.write( "sin(5x)cos(8x)-cos(5x)sin(8x)=-0.5<BR>\n" );
document.write( "sin(5x-8x)=-0.5<BR>\n" );
document.write( "sin(3x)=-0.5<BR>\n" );
document.write( "3x=210º<BR>\n" );
document.write( "x=70º </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );