document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1109042>Question 1109042</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sec A + tan A =2 find sin A + cos A ?\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 #724067 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=724067\">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=sec%28A%29%2Btan%28A%29=2 ALIGN=MIDDLE  ALT=\"sec%28A%29%2Btan%28A%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fcos%28A%29%2Bsin%28A%29%2Fcos%28A%29=2 ALIGN=MIDDLE  ALT=\"1%2Fcos%28A%29%2Bsin%28A%29%2Fcos%28A%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Bsin%28A%29%29%2Fcos%28A%29=2 ALIGN=MIDDLE  ALT=\"%281%2Bsin%28A%29%29%2Fcos%28A%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bsin%28A%29=2cos%28A%29 ALIGN=MIDDLE  ALT=\"1%2Bsin%28A%29=2cos%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29=2cos%28A%29-1 ALIGN=MIDDLE  ALT=\"sin%28A%29=2cos%28A%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let us say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28A%29=x ALIGN=MIDDLE  ALT=\"cos%28A%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29=%22+%22+%2B-+sqrt%281-x%5E2%29 ALIGN=MIDDLE  ALT=\"sin%28A%29=%22+%22+%2B-+sqrt%281-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting those expressions for sine and cosine,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22+%22+%2B-+sqrt%281-x%5E2%29=2x-1 ALIGN=MIDDLE  ALT=\"%22+%22+%2B-+sqrt%281-x%5E2%29=2x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Squaring both sides,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-x%5E2=4x%5E2%2B4x%2B1 ALIGN=MIDDLE  ALT=\"1-x%5E2=4x%5E2%2B4x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=4x%5E2%2B4x%2B1%2Bx%5E2-1 ALIGN=MIDDLE  ALT=\"0=4x%5E2%2B4x%2B1%2Bx%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=0=5x%5E2%2B4x ALIGN=MIDDLE  ALT=\"0=5x%5E2%2B4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x-4%29x=0%0D%0AThe+solutions+are+%7B%7B%7Bx=0 ALIGN=MIDDLE  ALT=\"%285x-4%29x=0%0D%0AThe+solutions+are+%7B%7B%7Bx=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4%2F5=0.8 ALIGN=MIDDLE  ALT=\"x=4%2F5=0.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "which translate into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29=0 ALIGN=MIDDLE  ALT=\"cos%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29=4%2F5=0.8 ALIGN=MIDDLE  ALT=\"cos%28x%29=4%2F5=0.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29=0 ALIGN=MIDDLE  ALT=\"cos%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not a solution of the original equation,<BR>\n" );
document.write( "because it would make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28A%29 ALIGN=MIDDLE  ALT=\"sec%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28A%29 ALIGN=MIDDLE  ALT=\"tan%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > undefined.<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28A%29=x=4%2F5=0.8 ALIGN=MIDDLE  ALT=\"cos%28A%29=x=4%2F5=0.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28A%29=1%2F0.8=1.25 ALIGN=MIDDLE  ALT=\"sec%28A%29=1%2F0.8=1.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29=%22+%22+%2B-+sqrt%281-x%5E2%29=%22+%22+%2B-+3%2F5=%22+%22+%2B-+0.6 ALIGN=MIDDLE  ALT=\"sin%28A%29=%22+%22+%2B-+sqrt%281-x%5E2%29=%22+%22+%2B-+3%2F5=%22+%22+%2B-+0.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29=-0.6 ALIGN=MIDDLE  ALT=\"sin%28A%29=-0.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > would make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28A%29=-0.6%2F0.8=-0.75 ALIGN=MIDDLE  ALT=\"tan%28A%29=-0.6%2F0.8=-0.75\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28A%29%2Btan%28A%29=1.25-0.75=0.5 ALIGN=MIDDLE  ALT=\"sec%28A%29%2Btan%28A%29=1.25-0.75=0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > so that is not a solution either.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28cos%28A%29=0.8%2Csin%28A%29=0.6%29 ALIGN=MIDDLE  ALT=\"system%28cos%28A%29=0.8%2Csin%28A%29=0.6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > makes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28A%29%2Btan%28A%29=1.25%2B0.75=2 ALIGN=MIDDLE  ALT=\"sec%28A%29%2Btan%28A%29=1.25%2B0.75=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >and is the solution.<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29%2Bcos%28A%29=0.8%2B0.6=highlight%281.4%29 ALIGN=MIDDLE  ALT=\"sin%28A%29%2Bcos%28A%29=0.8%2B0.6=highlight%281.4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
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