document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80734>Question 80734</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If (sec x-2)(2sec x-1)=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #57895 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=57895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sec+x-2%29%282sec+x-1%29=0 ALIGN=MIDDLE  ALT=\"%28sec+x-2%29%282sec+x-1%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=2sec%5E2%28x%29-sec%28x%29-4sec%28x%29%2B2=0 ALIGN=MIDDLE  ALT=\"2sec%5E2%28x%29-sec%28x%29-4sec%28x%29%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sec%5E2%28x%29-5sec%28x%29%2B2=0 ALIGN=MIDDLE  ALT=\"2sec%5E2%28x%29-5sec%28x%29%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sec%28x%29 ALIGN=MIDDLE  ALT=\"y=sec%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now factor to solve for y (note: this solver uses x instead of y):\r<BR>\n" );
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document.write( "ERROR Algebra::Solver::Engine::invoke_solver_noengine: solver not defined for name 'solving_by_factoring'.\n" );
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document.write( " <TR><TD >Error occurred executing solver 'solving_by_factoring' .</TD></TR>\n" );
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document.write( "Since we have the solutions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2F2 ALIGN=MIDDLE  ALT=\"y=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "we can say\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28x%29=1%2F2 ALIGN=MIDDLE  ALT=\"sec%28x%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28x%29=2 ALIGN=MIDDLE  ALT=\"sec%28x%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which is equivalent to \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fcos%28x%29=1%2F2 ALIGN=MIDDLE  ALT=\"1%2Fcos%28x%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fcos%28x%29=2 ALIGN=MIDDLE  ALT=\"1%2Fcos%28x%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now invert both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29=2%2F1 ALIGN=MIDDLE  ALT=\"cos%28x%29=2%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29=1%2F2 ALIGN=MIDDLE  ALT=\"cos%28x%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now take the arccosine of both sides to solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=cos%5E%28-1%29%282%2F1%29 ALIGN=MIDDLE  ALT=\"x=cos%5E%28-1%29%282%2F1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=cos%5E%28-1%29%281%2F2%29 ALIGN=MIDDLE  ALT=\"x=cos%5E%28-1%29%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the arccosine of 2 is undefined we must discard that answer. So our answer is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=pi%2F3%2Bpi%2An ALIGN=MIDDLE  ALT=\"x=pi%2F3%2Bpi%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" > where n is an integer\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=x=-pi%2F3%2Bpi%2An ALIGN=MIDDLE  ALT=\"x=-pi%2F3%2Bpi%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" > where n is an integer\r<BR>\n" );
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document.write( "which is equivalent in degrees:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=60%2B360%2An ALIGN=MIDDLE  ALT=\"x=60%2B360%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" > where n is an integer\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=x=-60%2B360%2An ALIGN=MIDDLE  ALT=\"x=-60%2B360%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" > where n is an integer </SPAN>\n" );
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