document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178825>Question 1178825</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve tan 2x + sec 2x = 6 over the interval [0, 2pi) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #808257 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=808257\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan+%282x%29+%2B+sec+%282x%29+=+6 ALIGN=MIDDLE  ALT=\"tan+%282x%29+%2B+sec+%282x%29+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > over the interval [0, 2pi)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%282x%29%2Fcos%282x%29+%2B+1%2Fcos%282x%29+=+6 ALIGN=MIDDLE  ALT=\"sin+%282x%29%2Fcos%282x%29+%2B+1%2Fcos%282x%29+=+6\"   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=%28sin+%282x%29%2B+1%29%2Fcos%282x%29+=+6+ ALIGN=MIDDLE  ALT=\"%28sin+%282x%29%2B+1%29%2Fcos%282x%29+=+6+\"   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=%28sin+%282x%29%2B+1%29=+6cos%282x%29 ALIGN=MIDDLE  ALT=\"%28sin+%282x%29%2B+1%29=+6cos%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ......square both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sin+%282x%29%2B+1%29%5E2=+%286cos%282x%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28sin+%282x%29%2B+1%29%5E2=+%286cos%282x%29%29%5E2\"   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=sin%5E2+%282x%29%2B2sin+%282x%29%2B+1=+36cos%5E2%282x%29 ALIGN=MIDDLE  ALT=\"sin%5E2+%282x%29%2B2sin+%282x%29%2B+1=+36cos%5E2%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...............since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E2%282x%29=1-sin%5E2%282x%29 ALIGN=MIDDLE  ALT=\"cos%5E2%282x%29=1-sin%5E2%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2+%282x%29%2B2sin+%282x%29%2B+1=+36%281-sin%5E2%282x%29%29 ALIGN=MIDDLE  ALT=\"sin%5E2+%282x%29%2B2sin+%282x%29%2B+1=+36%281-sin%5E2%282x%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=sin%5E2+%282x%29%2B2sin+%282x%29%2B+1=+36-36sin%5E2%282x%29 ALIGN=MIDDLE  ALT=\"sin%5E2+%282x%29%2B2sin+%282x%29%2B+1=+36-36sin%5E2%282x%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=sin%5E2+%282x%29%2B36sin%5E2%282x%29%2B2sin+%282x%29=36-1 ALIGN=MIDDLE  ALT=\"sin%5E2+%282x%29%2B36sin%5E2%282x%29%2B2sin+%282x%29=36-1\"   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=37sin%5E2%282x%29%2B2sin+%282x%29-35=0 ALIGN=MIDDLE  ALT=\"37sin%5E2%282x%29%2B2sin+%282x%29-35=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....use quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%282x%29=%28-2%2B-sqrt%282%5E2-4%2A37%28-35%29%29%29%2F%282%2A37%29 ALIGN=MIDDLE  ALT=\"sin+%282x%29=%28-2%2B-sqrt%282%5E2-4%2A37%28-35%29%29%29%2F%282%2A37%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=sin+%282x%29=%28-2%2B-sqrt%284%2B5180%29%29%2F74 ALIGN=MIDDLE  ALT=\"sin+%282x%29=%28-2%2B-sqrt%284%2B5180%29%29%2F74\"   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=sin+%282x%29=%28-2%2B-sqrt%285184%29%29%2F74 ALIGN=MIDDLE  ALT=\"sin+%282x%29=%28-2%2B-sqrt%285184%29%29%2F74\"   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=sin+%282x%29=%28-2%2B-72%29%2F74 ALIGN=MIDDLE  ALT=\"sin+%282x%29=%28-2%2B-72%29%2F74\"   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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%282x%29=%28-2%2B72%29%2F74=70%2F74=35%2F37 ALIGN=MIDDLE  ALT=\"sin+%282x%29=%28-2%2B72%29%2F74=70%2F74=35%2F37\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%282x%29=%28-2-72%29%2F74=-74%2F74=-1 ALIGN=MIDDLE  ALT=\"sin+%282x%29=%28-2-72%29%2F74=-74%2F74=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=sin%5E-1+%28-1%29 ALIGN=MIDDLE  ALT=\"2x=sin%5E-1+%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=-pi%2F2+ ALIGN=MIDDLE  ALT=\"2x=-pi%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-pi%2F4 ALIGN=MIDDLE  ALT=\"x=-pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (result in radians)\r<BR>\n" );
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document.write( "sin is negative in Q III or IV\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=215.54 ALIGN=MIDDLE  ALT=\"x=215.54\"   DISABLED_style= \"max-width:90%; height:auto;\" >°  (degrees)\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=sin%5E-1+%2835%2F37%29 ALIGN=MIDDLE  ALT=\"2x=sin%5E-1+%2835%2F37%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=1.24049897 ALIGN=MIDDLE  ALT=\"2x=1.24049897\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.24049897%2F2 ALIGN=MIDDLE  ALT=\"x=1.24049897%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.620249485 ALIGN=MIDDLE  ALT=\"x=0.620249485\"   DISABLED_style= \"max-width:90%; height:auto;\" >(result in radians)\r<BR>\n" );
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document.write( "in degrees:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=35.54 ALIGN=MIDDLE  ALT=\"x=35.54\"   DISABLED_style= \"max-width:90%; height:auto;\" >° (degrees)\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );