document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=325256>Question 325256</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to verify the following trigonometric identity, while only working only the left or right side of the equation and leaving either the right or left side unchanged.\r<BR>\n" );
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document.write( "1/1+cos theta + 1/1-cos theta = 2 + 2 cot^2 theta\r<BR>\n" );
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document.write( "I can make each side equal 2csc^2 theta currently, but have no clue how to make them equal working only one side.  Thanks for taking the time to look at this, its appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #232895 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=232895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{1+\cos(\theta)}+\frac{1}{1-\cos(\theta)}=2+2\cot^2{\theta}\"> ... Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1-\cos(\theta)}{(1+\cos(\theta)(1-\cos(\theta))}+\frac{1}{1-\cos(\theta)}=2+2\cot^2{\theta}\"> ... Multiply the first fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-cos%28theta%29%29%2F%281-cos%28theta%29%29 ALIGN=MIDDLE  ALT=\"%281-cos%28theta%29%29%2F%281-cos%28theta%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/rendertex.cgi?\LARGE \frac{1-\cos(\theta)}{(1+\cos(\theta)(1-\cos(\theta))}+\frac{1+\cos(\theta)}{(1+\cos(\theta)(1-\cos(\theta))}=2+2\cot^2{\theta}\"> ... Multiply the second fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Bcos%28theta%29%29%2F%281%2Bcos%28theta%29%29 ALIGN=MIDDLE  ALT=\"%281%2Bcos%28theta%29%29%2F%281%2Bcos%28theta%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/rendertex.cgi?\LARGE \frac{(1-\cos(\theta))+(1+\cos(\theta))}{(1+\cos(\theta)(1-\cos(\theta))}=2+2\cot^2{\theta}\"> ... Add the fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{2}{(1+\cos(\theta)(1-\cos(\theta))}=2+2\cot^2{\theta}\"> ... Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{2}{1-\cos^2(\theta)}=2+2\cot^2{\theta}\"> ... FOIL the denominator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{2}{\sin^2(\theta)}=2+2\cot^2{\theta}\"> ... Use the identity <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin^2(\theta) = 1-\cos^2(\theta)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{2\cdot 1}{\sin^2(\theta)}=2+2\cot^2{\theta}\"> ... Rewrite 2 as 2*1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{2\cdot \left(\sin^2(\theta)+\cos^2(\theta)\right)}{\sin^2(\theta)}=2+2\cot^2{\theta}\"> ... Use the identity <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin^2(\theta)+\cos^2(\theta) = 1\"> (replace the \"1\" with the left side)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{2\sin^2(\theta)+2\cos^2(\theta)}{\sin^2(\theta)}=2+2\cot^2{\theta}\"> ... Distribute.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{2\sin^2(\theta)}{\sin^2(\theta)}+\frac{2\cos^2(\theta)}{\sin^2(\theta)}=2+2\cot^2{\theta}\"> ... Break up the fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2+2\cot^2{\theta}=2+2\cot^2{\theta}\"> ... Reduce and use the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28theta%29=cos%28theta%29%2Fsin%28theta%29 ALIGN=MIDDLE  ALT=\"cot%28theta%29=cos%28theta%29%2Fsin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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