document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=187494>Question 187494</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I had a test today, and could not crack this problem I really would appreciate the help so I can understand it later on.\r<BR>\n" );
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document.write( "Prove:<BR>\n" );
document.write( "cotx*cosx=cotx-cosx\r<BR>\n" );
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document.write( "first i found a common denominator, but after that i was stuck. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #140534 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=140534\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm assuming that you want to prove that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28x%29%2Acos%28x%29=cot%28x%29-cos%28x%29 ALIGN=MIDDLE  ALT=\"cot%28x%29%2Acos%28x%29=cot%28x%29-cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an identity right?\r<BR>\n" );
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document.write( "There's a problem here, the equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28x%29%2Acos%28x%29=cot%28x%29-cos%28x%29 ALIGN=MIDDLE  ALT=\"cot%28x%29%2Acos%28x%29=cot%28x%29-cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "is NOT an identity (graph the two sides if you aren't sure)\r<BR>\n" );
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document.write( "For example, let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=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=cot%28x%29%2Acos%28x%29=cot%28x%29-cos%28x%29 ALIGN=MIDDLE  ALT=\"cot%28x%29%2Acos%28x%29=cot%28x%29-cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%281%29%2Acos%281%29=cot%281%29-cos%281%29 ALIGN=MIDDLE  ALT=\"cot%281%29%2Acos%281%29=cot%281%29-cos%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=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=%280.642%29%2A%280.540%29=0.642-0.540 ALIGN=MIDDLE  ALT=\"%280.642%29%2A%280.540%29=0.642-0.540\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate the given trig functions (note: I'm working in radian mode).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.34668=0.102 ALIGN=MIDDLE  ALT=\"0.34668=0.102\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. Clearly the two sides are NOT equal.\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.34668%3C%3E0.102 ALIGN=MIDDLE  ALT=\"0.34668%3C%3E0.102\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that the equation is NOT true for ALL values of \"x\". So the equation is NOT an identity.\r<BR>\n" );
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document.write( "So either there's a typo or you were supposed to disprove it being an identity. My guess would be that there's a typo in there somewhere.\r<BR>\n" );
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document.write( "Note: if you change the \"cot\" to \"csc\" and \"cos\" to \"sin\" on the right, you'll get  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28x%29%2Acos%28x%29=csc%28x%29-sin%28x%29 ALIGN=MIDDLE  ALT=\"cot%28x%29%2Acos%28x%29=csc%28x%29-sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is an identity </SPAN>\n" );
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