document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=105991>Question 105991</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/013195993X/algebrahomeworkh>Precalculus</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> prove the identity\r<BR>\n" );
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document.write( "cos theta sec theta/cot theta = tan theta\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77119 by </B><A HREF=/tutors/aboutme.mpl?userid=chitra><B>chitra(359)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=chitra><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=77119\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here i'm representing theta as x since writing theta everytime would be a tedious task.\r<BR>\n" );
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document.write( "So the given problem can be written as: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28Cos+x+Sec+x+%29%2FCot+x%29 ALIGN=MIDDLE  ALT=\"%28%28Cos+x+Sec+x+%29%2FCot+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = tan x\r<BR>\n" );
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document.write( "We know that Cos and Sec are reciprocal of each other. And also tan and cot are also reciprocate of each other. That is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Cos+x+=+%281%2FSec+x%29 ALIGN=MIDDLE  ALT=\"Cos+x+=+%281%2FSec+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Tan+x+=+%281%2FCot+x%29 ALIGN=MIDDLE  ALT=\"+Tan+x+=+%281%2FCot+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "so using the above in the given expression, we get: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28cosx+%2Asecx%29%2Fcotx%29 ALIGN=MIDDLE  ALT=\"%28%28cosx+%2Asecx%29%2Fcotx%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=%28Cosx%281%2FCosx%29%29%2F%281%2Ftanx%29 ALIGN=MIDDLE  ALT=\"%28Cosx%281%2FCosx%29%29%2F%281%2Ftanx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "The cos gets cancelled and we remain with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%281%2Ftan+x%29%29 ALIGN=MIDDLE  ALT=\"%281%2F%281%2Ftan+x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "so that is nothing but tan x\r<BR>\n" );
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document.write( "hence the solution.\r<BR>\n" );
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