document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178808>Question 1178808</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In this problem, we find all x with 0<x<2pi  such that tanx +secx =rad3\r<BR>\n" );
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document.write( "Use sin^2x+cos^2x=1 to find cosx. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #808233 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=808233\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "given: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%29+%2Bsec%28x%29+=sqrt%283%29 ALIGN=MIDDLE  ALT=\"tan%28x%29+%2Bsec%28x%29+=sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C+x+%3C+2pi ALIGN=MIDDLE  ALT=\"0%3C+x+%3C+2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We use the identity: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29+%2Bcos%5E2%28+x+%29=+1 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29+%2Bcos%5E2%28+x+%29=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  to find <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E2%28+x+%29=+1-sin%5E2%28x%29+ ALIGN=MIDDLE  ALT=\"cos%5E2%28+x+%29=+1-sin%5E2%28x%29+\"   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=cos%5E2%28+x+%29=%28+1-sin%28x%29%29%28+1%2Bsin%28x%29%29 ALIGN=MIDDLE  ALT=\"cos%5E2%28+x+%29=%28+1-sin%28x%29%29%28+1%2Bsin%28x%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=cos%5E2%28+x+%29%2F%28+1-sin%28x%29%29=%28+1%2Bsin%28x%29%29 ALIGN=MIDDLE  ALT=\"cos%5E2%28+x+%29%2F%28+1-sin%28x%29%29=%28+1%2Bsin%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....1)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%29=sin%28x%29%2Fcos%28x%29 ALIGN=MIDDLE  ALT=\"tan%28x%29=sin%28x%29%2Fcos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28x%29=1%2Fcos%28x%29 ALIGN=MIDDLE  ALT=\"sec%28x%29=1%2Fcos%28x%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%28x%29%2Fcos%28x%29+%2B1%2Fcos%28x%29+=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sin%28x%29%2Fcos%28x%29+%2B1%2Fcos%28x%29+=sqrt%283%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=%28sin%28x%29%2B1%29%2Fcos%28x%29+=sqrt%283%29 ALIGN=MIDDLE  ALT=\"%28sin%28x%29%2B1%29%2Fcos%28x%29+=sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+1%2Bsin%28x%29%29 ALIGN=MIDDLE  ALT=\"%28+1%2Bsin%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from 1)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cos%5E2%28+x+%29%2F%28+1-sin%28x%29%29%29%2Fcos%28x%29+=sqrt%283%29 ALIGN=MIDDLE  ALT=\"%28cos%5E2%28+x+%29%2F%28+1-sin%28x%29%29%29%2Fcos%28x%29+=sqrt%283%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=cos%28x%29%2F%281+-+sin%28x%29%29=sqrt%283%29 ALIGN=MIDDLE  ALT=\"cos%28x%29%2F%281+-+sin%28x%29%29=sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "use the identity: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29+%2Bcos%5E2%28+x+%29=+1 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29+%2Bcos%5E2%28+x+%29=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  to find <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29=sqrt%281-cos%5E2%28+x+%29%29 ALIGN=MIDDLE  ALT=\"sin%28x%29=sqrt%281-cos%5E2%28+x+%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=cos%28x%29%2F%281+-+sqrt%281-cos%5E2%28+x+%29%29%29=sqrt%283%29 ALIGN=MIDDLE  ALT=\"cos%28x%29%2F%281+-+sqrt%281-cos%5E2%28+x+%29%29%29=sqrt%283%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=cos%28x%29=%281+-+sqrt%281-cos%5E2%28+x+%29%29%29%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"cos%28x%29=%281+-+sqrt%281-cos%5E2%28+x+%29%29%29%2Asqrt%283%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=cos%28x%29%2Fsqrt%283%29=1+-+sqrt%281-cos%5E2%28+x+%29%29 ALIGN=MIDDLE  ALT=\"cos%28x%29%2Fsqrt%283%29=1+-+sqrt%281-cos%5E2%28+x+%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=cos%28x%29%2Fsqrt%283%29-1=+-+sqrt%281-cos%5E2%28+x+%29%29 ALIGN=MIDDLE  ALT=\"cos%28x%29%2Fsqrt%283%29-1=+-+sqrt%281-cos%5E2%28+x+%29%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=%28cos%28x%29%2Fsqrt%283%29-1%29%5E2=+%28-+sqrt%281-cos%5E2%28+x+%29%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28cos%28x%29%2Fsqrt%283%29-1%29%5E2=+%28-+sqrt%281-cos%5E2%28+x+%29%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=%28cos%28x%29-sqrt%283%29%29%2F%28sqrt%283%29%29%5E2=+1-cos%5E2%28+x+%29 ALIGN=MIDDLE  ALT=\"%28cos%28x%29-sqrt%283%29%29%2F%28sqrt%283%29%29%5E2=+1-cos%5E2%28+x+%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=%28cos%28x%29-sqrt%283%29%29%5E2%2F3=+1-cos%5E2%28+x+%29 ALIGN=MIDDLE  ALT=\"%28cos%28x%29-sqrt%283%29%29%5E2%2F3=+1-cos%5E2%28+x+%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=cos%5E2%28x%29-2cos%28x%29%2Asqrt%283%29%2B3=+3-3cos%5E2%28+x+%29 ALIGN=MIDDLE  ALT=\"cos%5E2%28x%29-2cos%28x%29%2Asqrt%283%29%2B3=+3-3cos%5E2%28+x+%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=cos%5E2%28x%29%2B3cos%5E2%28+x+%29-2cos%28x%29%2Asqrt%283%29%2B3-+3=0 ALIGN=MIDDLE  ALT=\"cos%5E2%28x%29%2B3cos%5E2%28+x+%29-2cos%28x%29%2Asqrt%283%29%2B3-+3=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=4cos%5E2%28+x+%29-2cos%28x%29%2Asqrt%283%29=0 ALIGN=MIDDLE  ALT=\"4cos%5E2%28+x+%29-2cos%28x%29%2Asqrt%283%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%28x%29%282cos%28+x+%29-sqrt%283%29%29=0 ALIGN=MIDDLE  ALT=\"2cos%28x%29%282cos%28+x+%29-sqrt%283%29%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( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2cos%28x%29=0 ALIGN=MIDDLE  ALT=\"2cos%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <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;\" >\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2cos%28+x+%29-sqrt%283%29=0 ALIGN=MIDDLE  ALT=\"2cos%28+x+%29-sqrt%283%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2cos%28+x+%29=sqrt%283%29 ALIGN=MIDDLE  ALT=\"2cos%28+x+%29=sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28+x+%29=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"cos%28+x+%29=sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan+%28x%29 ALIGN=MIDDLE  ALT=\"tan+%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <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;\" > are positive, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > lies in the first quadrant, and in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29%2Fcos%28x%29+%2B1%2Fcos%28x%29+=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sin%28x%29%2Fcos%28x%29+%2B1%2Fcos%28x%29+=sqrt%283%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=cos%28x%29=0 ALIGN=MIDDLE  ALT=\"cos%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is denominator, so disregard this solution\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%28x+%29=+sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"cos+%28x+%29=+sqrt%283%29%2F2\"   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=x=+cos%5E-1%28sqrt%283%29%2F2+%29 ALIGN=MIDDLE  ALT=\"x=+cos%5E-1%28sqrt%283%29%2F2+%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=x=+pi%2F6 ALIGN=MIDDLE  ALT=\"x=+pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > (result in radians)-> your solution\r<BR>\n" );
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document.write( "convert to degrees\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+30 ALIGN=MIDDLE  ALT=\"+x+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" >° (degrees)\r<BR>\n" );
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