document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=645659>Question 645659</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I would love love love help proving the following identity:\r<BR>\n" );
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document.write( "1 + tan(theta)/ 1 + cot(theta) = 1- tan(theta)/cot(theta) - 1\r<BR>\n" );
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document.write( "thank you much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #405578 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=405578\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "I should make you repost this because your rendering of the equation is so ambiguous; there are several ways to interpret what does or does not go into each numerator and denominator. But since my first guess at what you meant works out, I'll give you a break this time.  Next time use sufficient parentheses so that it is clear what you mean.  I'm interpreting your input as:\r<BR>\n" );
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document.write( "(1 + tan(t))/( 1 + cot(t)) = (1 - tan(t))/(cot(t) - 1)\r<BR>\n" );
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document.write( "BTW, there is no need to spell out theta.  You can use any variable since it all comes out in the wash at the end anyway.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{1\ +\ \tan(\theta)}{1\ +\ \cot(\theta)}\ \equiv^?\ \frac{1\ -\ \tan(\theta)}{\cot(\theta)\ -\ 1}\">\r<BR>\n" );
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document.write( "Use the identities for tangent and cotangent in terms of sine and cosine:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{1\ +\ \frac{\sin(\theta)}{\cos(\theta)}}{1\ +\ \frac{\cos(\theta)}{\sin(\theta)}}\ \equiv^?\ \frac{1\ -\ \frac{\sin(\theta)}{\cos(\theta)}}{\frac{\cos(\theta)}{\sin(\theta)}\ -\ 1}\">\r<BR>\n" );
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document.write( "Apply the LCD for each numerator and denominator expression:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\frac{\cos(\theta)\ +\ \sin(\theta)}{\cos(\theta)}}{\frac{\sin(\theta)\ +\ \cos(\theta)}{\sin(\theta)}}\ \equiv^?\ \frac{\frac{\cos(\theta)\ -\ \sin(\theta)}{\cos(\theta)}}{\frac{\cos(\theta)\ -\ \sin(\theta)}{\sin(\theta)}}\">\r<BR>\n" );
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document.write( "Next, invert and multiply to divide on each side.  You can write it out for yourself if you want to verify, but note that on each side of the equation the numerator of the numerator is equal to the numerator of the denominator, hence, when you invert and multiply on both sides you are left with:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\sin(\theta)}{\cos(\theta)}\ \equiv\ \frac{\sin(\theta)}{\cos(\theta)}\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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