document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=302828>Question 302828</A>: <I><SPAN STYLE=\"word-break: break-all;\">  3cos^2 2x - 2sin^2 2x = 2 - 4sin2x\r<BR>\n" );
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document.write( "find all the angles between 0degrees to 180degrees inclusive which satisfy equation\r<BR>\n" );
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document.write( "--x-x-x-x-x-x-x-x-x--\r<BR>\n" );
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document.write( "express 1/ (x-3)(2x +1) as partial fractions\r<BR>\n" );
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document.write( "hence evaluate (cant really draw it out but.... evaluate definite integral 7 on top, 4 below. 1/(x-3)(2x +1)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #217102 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=217102\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=sin%282x%29 ALIGN=MIDDLE  ALT=\"S=sin%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=cos%282x%29 ALIGN=MIDDLE  ALT=\"C=cos%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to reduce the clutter,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3C%5E2-2S%5E2+=+2+-+4S ALIGN=MIDDLE  ALT=\"3C%5E2-2S%5E2+=+2+-+4S\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3C%5E2-2S%5E2%2B4S-2+=0 ALIGN=MIDDLE  ALT=\"3C%5E2-2S%5E2%2B4S-2+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Remember that <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5E2%2BS%5E2=1 ALIGN=MIDDLE  ALT=\"C%5E2%2BS%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5E2=1-S%5E2 ALIGN=MIDDLE  ALT=\"C%5E2=1-S%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3C%5E2=3-3S%5E2 ALIGN=MIDDLE  ALT=\"3C%5E2=3-3S%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-3S%5E2%29-2S%5E2%2B4S-2=0 ALIGN=MIDDLE  ALT=\"%283-3S%5E2%29-2S%5E2%2B4S-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5S%5E2%2B4S%2B1=0 ALIGN=MIDDLE  ALT=\"-5S%5E2%2B4S%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5S%5E2-4S-1=0 ALIGN=MIDDLE  ALT=\"5S%5E2-4S-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can factor,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285S%2B1%29%28S-1%29=0 ALIGN=MIDDLE  ALT=\"%285S%2B1%29%28S-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5S%2B1=0 ALIGN=MIDDLE  ALT=\"5S%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=-1%2F5 ALIGN=MIDDLE  ALT=\"S=-1%2F5\"   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=-1%2F5 ALIGN=MIDDLE  ALT=\"sin%282x%29=-1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S-1=0 ALIGN=MIDDLE  ALT=\"S-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=1 ALIGN=MIDDLE  ALT=\"S=1\"   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=1 ALIGN=MIDDLE  ALT=\"sin%282x%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I leave those to you to complete.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Partial fractions.<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F+%28%28x-3%29%282x+%2B1%29%29+=A%2F%28x-3%29%2BB%2F%282x%2B1%29 ALIGN=MIDDLE  ALT=\"1%2F+%28%28x-3%29%282x+%2B1%29%29+=A%2F%28x-3%29%2BB%2F%282x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%282x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%282x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=A%282x%2B1%29%2BB%28x-3%29 ALIGN=MIDDLE  ALT=\"1=A%282x%2B1%29%2BB%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282Ax%2BBx%29%2B%28A-3B%29=1 ALIGN=MIDDLE  ALT=\"%282Ax%2BBx%29%2B%28A-3B%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Leads to two equations,<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2A%2BB=0 ALIGN=MIDDLE  ALT=\"2A%2BB=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A-3B=1 ALIGN=MIDDLE  ALT=\"A-3B=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply eq.1 by 3 and add the two together to solve for A.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6A%2B3B%2BA-3B=1 ALIGN=MIDDLE  ALT=\"6A%2B3B%2BA-3B=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7A=1 ALIGN=MIDDLE  ALT=\"7A=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=1%2F7 ALIGN=MIDDLE  ALT=\"A=1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then use either equation to solve for B.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2A%2BB=0 ALIGN=MIDDLE  ALT=\"2A%2BB=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-2A=-2%2F7 ALIGN=MIDDLE  ALT=\"B=-2A=-2%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F+%28%28x-3%29%282x+%2B1%29%29+=%281%2F7%29%2A%281%2F%28x-3%29%29-%282%2F7%29%2A%281%2F%282x%2B1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If you integrate you'll get<BR>\n" );
document.write( "INT=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F7%29ln%28x-3%29-%282%2F7%29ln%282x%2B1%29 ALIGN=MIDDLE  ALT=\"%281%2F7%29ln%28x-3%29-%282%2F7%29ln%282x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > evaluated between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "I leave those to you to complete. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );