document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1128735>Question 1128735</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all exact solutions on <BR>\n" );
document.write( "[0, 2&#960;).<BR>\n" );
document.write( "(Enter your answers as a comma-separated list.) <BR>\n" );
document.write( "2 tan2(t) = 3 sec(t)\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #745222 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=745222\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( " If we restrict the domain of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > to [<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >) then \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=pi%2F3 ALIGN=MIDDLE  ALT=\"t=pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5pi%2F3 ALIGN=MIDDLE  ALT=\"5pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2tan%5E2%28t%29+=+3+sec%28t%29+ ALIGN=MIDDLE  ALT=\"2tan%5E2%28t%29+=+3+sec%28t%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sin%5E2%28t%29%2Fcos%5E2%28t%29+=+3%281%2Fcos%28t%29+%29 ALIGN=MIDDLE  ALT=\"2sin%5E2%28t%29%2Fcos%5E2%28t%29+=+3%281%2Fcos%28t%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sin%5E2%28t%29+=+3+%28cos%5E2%28t%29%2Fcos%28t%29+%29 ALIGN=MIDDLE  ALT=\"2sin%5E2%28t%29+=+3+%28cos%5E2%28t%29%2Fcos%28t%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sin%5E2%28t%29+=+3+cos%28t%29+ ALIGN=MIDDLE  ALT=\"2sin%5E2%28t%29+=+3+cos%28t%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%281-cos%5E2%28t%29%29+=+3+cos%28t%29 ALIGN=MIDDLE  ALT=\"2%281-cos%5E2%28t%29%29+=+3+cos%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+-2cos%5E2%28t%29+=+3+cos%28t%29 ALIGN=MIDDLE  ALT=\"2+-2cos%5E2%28t%29+=+3+cos%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2cos%5E2%28t%29+%2B3+cos%28t%29+-2=0 ALIGN=MIDDLE  ALT=\"2cos%5E2%28t%29+%2B3+cos%28t%29+-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > .......factor\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2cos%5E2%28t%29+%2B4+cos%28t%29-cos%28t%29+-2=0 ALIGN=MIDDLE  ALT=\"2cos%5E2%28t%29+%2B4+cos%28t%29-cos%28t%29+-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282cos%5E2%28t%29+%2B4+cos%28t%29%29-%28cos%28t%29+%2B2%29=0 ALIGN=MIDDLE  ALT=\"%282cos%5E2%28t%29+%2B4+cos%28t%29%29-%28cos%28t%29+%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2cos%28t%29%28cos%28t%29+%2B2%29-%28cos%28t%29+%2B2%29=0 ALIGN=MIDDLE  ALT=\"2cos%28t%29%28cos%28t%29+%2B2%29-%28cos%28t%29+%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282cos%28t%29-1%29%28cos%28t%29+%2B2%29=0 ALIGN=MIDDLE  ALT=\"%282cos%28t%29-1%29%28cos%28t%29+%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "case 1:\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2cos%28t%29-1=0 ALIGN=MIDDLE  ALT=\"2cos%28t%29-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > -><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cos%28t%29=1%2F2 ALIGN=MIDDLE  ALT=\"+cos%28t%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=pi%2F3 ALIGN=MIDDLE  ALT=\"t=pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=5pi%2F3 ALIGN=MIDDLE  ALT=\"t=5pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > assuming [<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "case 2:\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28t%29+%2B2%29=0 ALIGN=MIDDLE  ALT=\"cos%28t%29+%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28t%29+=-2 ALIGN=MIDDLE  ALT=\"cos%28t%29+=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  BUT, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28t%29 ALIGN=MIDDLE  ALT=\"cos%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is element of [<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >] for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=all ALIGN=MIDDLE  ALT=\"all\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t ALIGN=MIDDLE  ALT=\"+t\"   DISABLED_style= \"max-width:90%; height:auto;\" >; therefore, this case is extraneous and we will disregard it\r<BR>\n" );
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