document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=86952>Question 86952</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me to answer this problem: derive the identity: cot^2 A + 1 = csc ^2 A . </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #62919 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20060)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=62919\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> please help me to answer this problem: derive the identity:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%5E2A+%2B+1+=+csc%5E2A ALIGN=MIDDLE  ALT=\"cot%5E2A+%2B+1+=+csc%5E2A\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
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document.write( "Draw a standard labeled right triangle:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28200%2C200%2C-1%2C10%2C-1%2C15%2C+triangle%280%2C0%2C8%2C0%2C8%2C15%29%2C%0D%0Alocate%288.5%2C7.5%2C%22a%22%29%2C+locate%282.7%2C7.5%2C%22c%22%29%2C+locate%28-.5%2C0%2C%22A%22%29%2C%0D%0Alocate%288.5%2C0%2C%22C%22%29%2C+locate%288.5%2C15%2C%22B%22%29%2C+locate%284%2C-.5%2C%22b%22%29%2C%0D%0Arectangle%287.5%2C0%2C8%2C.5%29%0D%0A%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "By the Pythagorean theorem:\r<BR>\n" );
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document.write( "             <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2 ALIGN=MIDDLE  ALT=\"b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2 ALIGN=MIDDLE  ALT=\"c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide every term by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%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=a%5E2%2Fa%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Fa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2Fa%5E2 ALIGN=MIDDLE  ALT=\"b%5E2%2Fa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2%2Fa%5E2 ALIGN=MIDDLE  ALT=\"c%5E2%2Fa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The first term, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Fa%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Fa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is just 1.\r<BR>\n" );
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document.write( "                     1 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2Fa%5E2 ALIGN=MIDDLE  ALT=\"b%5E2%2Fa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2%2Fa%5E2 ALIGN=MIDDLE  ALT=\"c%5E2%2Fa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we can write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2Fa%5E2 ALIGN=MIDDLE  ALT=\"b%5E2%2Fa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%2Fa%29%5E2 ALIGN=MIDDLE  ALT=\"%28b%2Fa%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and<BR>\n" );
document.write( "we can write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2%2Fa%5E2 ALIGN=MIDDLE  ALT=\"c%5E2%2Fa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28c%2Fa%29%5E2 ALIGN=MIDDLE  ALT=\"%28c%2Fa%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, \r<BR>\n" );
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document.write( "                     1 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%2Fa%29%5E2 ALIGN=MIDDLE  ALT=\"%28b%2Fa%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28c%2Fa%29%5E2 ALIGN=MIDDLE  ALT=\"%28c%2Fa%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Fa ALIGN=MIDDLE  ALT=\"b%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28adjacent%29%2F%28opposite%29 ALIGN=MIDDLE  ALT=\"%28adjacent%29%2F%28opposite%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28A%29 ALIGN=MIDDLE  ALT=\"cot%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2Fa ALIGN=MIDDLE  ALT=\"c%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28hypotenuse%29%2F%28opposite%29 ALIGN=MIDDLE  ALT=\"%28hypotenuse%29%2F%28opposite%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=csc%28A%29 ALIGN=MIDDLE  ALT=\"csc%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "so, upon substituting these, we have<BR>\n" );
document.write( "              <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2B+cot%5E2A+=+csc%5E2A ALIGN=MIDDLE  ALT=\"1+%2B+cot%5E2A+=+csc%5E2A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or reversing the terms on the left:<BR>\n" );
document.write( "             <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%5E2A+%2B+1+=+csc%5E2A ALIGN=MIDDLE  ALT=\"cot%5E2A+%2B+1+=+csc%5E2A\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Edwin<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\"> </SPAN>\n" );
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