document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1052209>Question 1052209</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this problem!\r<BR>\n" );
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document.write( "If cosx = 1/5. Find all possible values of secx - tanx/ sinx.\r<BR>\n" );
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document.write( "Now, the answer at the back of the book is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2825sqrt%286%29+-+60%29%2F12 ALIGN=MIDDLE  ALT=\"%2825sqrt%286%29+-+60%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > ; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-25sqrt%286%29+-+60%29%2F12 ALIGN=MIDDLE  ALT=\"%28-25sqrt%286%29+-+60%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I just can't quite get there. I know you have to turn everything into cos, because that is what you have a value for. \r<BR>\n" );
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document.write( "So I got: 1/cosx - sinx/cosx for the numerator. You can add these because the denominators are the same. So it would be: 1 - sinx/cosx. And all of this over sinx. \r<BR>\n" );
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document.write( "Then I thought, hmmmm, what if I were to multiply the numerator and denominator by sinx. That would give me: sinx - sin^2x / cosx / sin^2x. And sin^2x = 1 - cos^2x, so that takes care of that, but I still have that sinx at the beginning that I can't get rid of. :(   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #667642 by </B><A HREF=/tutors/aboutme.mpl?userid=advanced_Learner><B>advanced_Learner(501)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=advanced_Learner><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=advanced_Learner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=667642\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this problem!\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cosx ALIGN=MIDDLE  ALT=\"cosx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5 ALIGN=MIDDLE  ALT=\"1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Find all possible values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28secx+-+tanx%29%2F+%28sinx%29 ALIGN=MIDDLE  ALT=\"%28secx+-+tanx%29%2F+%28sinx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is long but bear with me.\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29 ALIGN=MIDDLE  ALT=\"cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5 ALIGN=MIDDLE  ALT=\"1%2F5\"   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=cos%5E2%28x%29 ALIGN=MIDDLE  ALT=\"cos%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29\"   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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F5%29%5E2 ALIGN=MIDDLE  ALT=\"%281%2F5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29\"   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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F25%29 ALIGN=MIDDLE  ALT=\"%281%2F25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29\"   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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29\"   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;\" >-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F25%29 ALIGN=MIDDLE  ALT=\"%281%2F25%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%28x%29 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F25 ALIGN=MIDDLE  ALT=\"25%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F25%29 ALIGN=MIDDLE  ALT=\"%281%2F25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "thus \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29 ALIGN=MIDDLE  ALT=\"sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2824%2F25%29 ALIGN=MIDDLE  ALT=\"sqrt%2824%2F25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29 ALIGN=MIDDLE  ALT=\"sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2824%2F25%29 ALIGN=MIDDLE  ALT=\"sqrt%2824%2F25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "remember that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2824%2F25%29 ALIGN=MIDDLE  ALT=\"sqrt%2824%2F25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Asqrt%286%29%29%2F%285%29 ALIGN=MIDDLE  ALT=\"%282%2Asqrt%286%29%29%2F%285%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=%28secx+-+tanx%29%2F+%28sinx%29 ALIGN=MIDDLE  ALT=\"%28secx+-+tanx%29%2F+%28sinx%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=%28%281%2Fcos%28x%29%29+-+%28sin%28x%29%29%2F%28cos%28x%29%29%29 ALIGN=MIDDLE  ALT=\"%28%281%2Fcos%28x%29%29+-+%28sin%28x%29%29%2F%28cos%28x%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28sin%28x%29%29%29 ALIGN=MIDDLE  ALT=\"%281%2F%28sin%28x%29%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=%28%281-sinx%29%2Fcos%28x%29%29 ALIGN=MIDDLE  ALT=\"%28%281-sinx%29%2Fcos%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28sin%28x%29%29%29 ALIGN=MIDDLE  ALT=\"%281%2F%28sin%28x%29%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=%28%281-sqrt%2824%2F25%29%29%2F%281%2F5%29%29 ALIGN=MIDDLE  ALT=\"%28%281-sqrt%2824%2F25%29%29%2F%281%2F5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28sqrt%2824%2F25%29%29%29 ALIGN=MIDDLE  ALT=\"%281%2F%28sqrt%2824%2F25%29%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=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281-sqrt%2824%2F25%29%29%29 ALIGN=MIDDLE  ALT=\"%28%281-sqrt%2824%2F25%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28sqrt%2824%2F25%29%29%29 ALIGN=MIDDLE  ALT=\"%281%2F%28sqrt%2824%2F25%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "simplify to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Asqrt%286%29%2A25-24%2A5%29%2F%2824%29 ALIGN=MIDDLE  ALT=\"%282%2Asqrt%286%29%2A25-24%2A5%29%2F%2824%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=%282%2Asqrt%286%29%2A25-120%29%2F%2824%29 ALIGN=MIDDLE  ALT=\"%282%2Asqrt%286%29%2A25-120%29%2F%2824%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=%28sqrt%286%29%2A25-60%29%2F%2812%29 ALIGN=MIDDLE  ALT=\"%28sqrt%286%29%2A25-60%29%2F%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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