document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=425935>Question 425935</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi am stuck on the cotangent formula for triangles<BR>\n" );
document.write( "how do we get from number 1 to number 2 \r<BR>\n" );
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document.write( "1. m{cot &#945;-cot&#952;} = n{cot &#946; + cot &#952;}\r<BR>\n" );
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document.write( "2. (m+n) cot &#952;  = m cot &#945; - n cot &#946; </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #296414 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=296414\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this looks like it's straight algebra manipulation.\r<BR>\n" );
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document.write( "let a = cot(alpha)<BR>\n" );
document.write( "let b = cot(beta)<BR>\n" );
document.write( "let t = cot(theta)\r<BR>\n" );
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document.write( "t is equal to the lower case T, no to be confused with + which is the plus sign.\r<BR>\n" );
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document.write( "you start with m*(a-t) = n*(b+t)\r<BR>\n" );
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document.write( "multiply out each factor to get:\r<BR>\n" );
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document.write( "m*a - m*t = n*b + n*t\r<BR>\n" );
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document.write( "add m*t to  both sides of the equation and subtract n*b from both sides of the equation to get:\r<BR>\n" );
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document.write( "m*a - n*b = m*t + n*t\r<BR>\n" );
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document.write( "factor to get:\r<BR>\n" );
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document.write( "m*a - n*b = (m+n)*t\r<BR>\n" );
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document.write( "commute to get:\r<BR>\n" );
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document.write( "(m+n)*t = m*a - n*b\r<BR>\n" );
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document.write( "substitute for t,a,b to get:\r<BR>\n" );
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document.write( "(m+n) * cot (theta) = m*cot(alpha) - n*cot(beta)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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