document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=962295>Question 962295</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the exact value of the expression:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin+%28+pi%2F6+%29+%2B+tan%5E2+%28+pi%2F5+%29.%0D%0A ALIGN=MIDDLE  ALT=\"+sin+%28+pi%2F6+%29+%2B+tan%5E2+%28+pi%2F5+%29.%0D%0A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I am familiar with some of the trigonometric identities, however for some reason this one has me stumped.  I attempted to convert them into their reciprocals, cosecant and cotangent in order to try and see if it lined up with the following identity.\r<BR>\n" );
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document.write( "csc^2(x) = cot^2(x) + 1 \r<BR>\n" );
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document.write( "That did not seem to work.  I think what's messing me up here is the tangent being squared and the sine is not.  Unfortunately, with this expression, I'm unsure of where to start. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #587900 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=587900\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I do not think you need to use identities to solve this\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin+%28+pi%2F6+%29+%2B+tan%5E2+%28+pi%2F5+%29 ALIGN=MIDDLE  ALT=\"+sin+%28+pi%2F6+%29+%2B+tan%5E2+%28+pi%2F5+%29\"   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=+sin+%28+pi%2F6+%29=1%2F2 ALIGN=MIDDLE  ALT=\"+sin+%28+pi%2F6+%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%5E2+%28+pi%2F5+%29=tan+%28+pi%2F5+%29%2Atan%28+pi%2F5+%29 ALIGN=MIDDLE  ALT=\"tan%5E2+%28+pi%2F5+%29=tan+%28+pi%2F5+%29%2Atan%28+pi%2F5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan+%28+pi%2F5+%29=sqrt%285-2+sqrt%285%29%29 ALIGN=MIDDLE  ALT=\"tan+%28+pi%2F5+%29=sqrt%285-2+sqrt%285%29%29\"   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=tan%5E2+%28+pi%2F5+%29=%28sqrt%285-2sqrt%285%29%29%29%5E2 ALIGN=MIDDLE  ALT=\"tan%5E2+%28+pi%2F5+%29=%28sqrt%285-2sqrt%285%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=tan%5E2+%28+pi%2F5+%29=5-2sqrt%285%29 ALIGN=MIDDLE  ALT=\"tan%5E2+%28+pi%2F5+%29=5-2sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F2+%2B+%285-2sqrt%285%29%29 ALIGN=MIDDLE  ALT=\"+1%2F2+%2B+%285-2sqrt%285%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%2F2+%2B+10%2F2-2sqrt%285%29%29 ALIGN=MIDDLE  ALT=\"+1%2F2+%2B+10%2F2-2sqrt%285%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=+11%2F2-2sqrt%285%29%29 ALIGN=MIDDLE  ALT=\"+11%2F2-2sqrt%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the exact value of the expression is:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F2-2sqrt%285%29 ALIGN=MIDDLE  ALT=\"11%2F2-2sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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