document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193298>Question 1193298</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the following equation:\r<BR>\n" );
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document.write( "tan x + 1/tanx= secx/six\r<BR>\n" );
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document.write( "a. verify that the equation is true for x = 2Π/3<BR>\n" );
document.write( "b. Prove the equation  is an identity </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825316 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=825316\">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=tan+%28x%29+%2B+1%2Ftan%28x%29=+sec%28x%29%2Fsin%28x%29 ALIGN=MIDDLE  ALT=\"tan+%28x%29+%2B+1%2Ftan%28x%29=+sec%28x%29%2Fsin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a. verify that the equation is true for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2pi%2F3 ALIGN=MIDDLE  ALT=\"x+=+2pi%2F3\"   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=tan%282pi%2F3%29%2B1%2Ftan%282pi%2F3%29=+sec%282pi%2F3%29%2Fsin%282pi%2F3%29 ALIGN=MIDDLE  ALT=\"tan%282pi%2F3%29%2B1%2Ftan%282pi%2F3%29=+sec%282pi%2F3%29%2Fsin%282pi%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan+%282pi%2F3%29=+-sqrt%283%29 ALIGN=MIDDLE  ALT=\"tan+%282pi%2F3%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=sec%282pi%2F3%29=-2 ALIGN=MIDDLE  ALT=\"sec%282pi%2F3%29=-2\"   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%282pi%2F3%29=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"sin%282pi%2F3%29=sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "substituting in equation above, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%283%29+%2B+1%2F%28-sqrt%283%29%29=+-2%2F%28sqrt%283%29%2F2%29 ALIGN=MIDDLE  ALT=\"-sqrt%283%29+%2B+1%2F%28-sqrt%283%29%29=+-2%2F%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=%28-%28sqrt%283%29+%29%5E2%2B+1%29%2F%28-sqrt%283%29%29=+-4%2F%28sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"%28-%28sqrt%283%29+%29%5E2%2B+1%29%2F%28-sqrt%283%29%29=+-4%2F%28sqrt%283%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=-%283%2B+1%29%2F%28-sqrt%283%29%29=+-4%2F%28sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"-%283%2B+1%29%2F%28-sqrt%283%29%29=+-4%2F%28sqrt%283%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=-4%2F%28-sqrt%283%29%29=+-4%2F%28sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"-4%2F%28-sqrt%283%29%29=+-4%2F%28sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =>both sides same, the equation is true for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2pi%2F3 ALIGN=MIDDLE  ALT=\"x+=+2pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b. Prove the equation is an identity\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan+%28x%29+%2B+1%2Ftan%28x%29=+sec%28x%29%2Fsin%28x%29 ALIGN=MIDDLE  ALT=\"tan+%28x%29+%2B+1%2Ftan%28x%29=+sec%28x%29%2Fsin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...... use identity: <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=%28tan%5E2+%28x%29+%2B+1%29%2Ftan%28x%29=+%281%2Fcos%28x%29%29%2Fsin%28x%29 ALIGN=MIDDLE  ALT=\"%28tan%5E2+%28x%29+%2B+1%29%2Ftan%28x%29=+%281%2Fcos%28x%29%29%2Fsin%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=%28sin%5E2+%28x%29%2Fcos%5E2%28x%29+%2B+1%29%2F%28sin%28x%29%2Fcos%28x%29%29=+%281%2Fcos%28x%29%29%2Fsin%28x%29 ALIGN=MIDDLE   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%28sin%5E2%28x%29%2Bcos%5E2%28x%29%29%2Fcos%5E2%28x%29%29%2F%28sin%28x%29%2Fcos%28x%29%29=1%2F%28cos%28x%29sin%28x%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29%2B+cos%5E2%28x%29=1 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29%2B+cos%5E2%28x%29=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%2Fcos%28x%29%29%2F%28sin%28x%29%2F1%29=+1%2F%28cos%28x%29sin%28x%29%29 ALIGN=MIDDLE  ALT=\"%281%2Fcos%28x%29%29%2F%28sin%28x%29%2F1%29=+1%2F%28cos%28x%29sin%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=1%2F%28cos%28x%29sin%28x%29%29=+1%2F%28cos%28x%29sin%28x%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28cos%28x%29sin%28x%29%29=+1%2F%28cos%28x%29sin%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=>identity proven\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );