document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=96996>Question 96996</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If cotA + cotB + cotC=sqrt3 then prove that the triangle is equilateral. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #70606 by </B><A HREF=/tutors/aboutme.mpl?userid=mathslover><B>mathslover(157)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathslover><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=mathslover><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=70606\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given cotA + cotB + cotC = sqrt3<BR>\n" );
document.write( "to prove triangle ABC is equilateral\r<BR>\n" );
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document.write( "we prove this by assuming ABC to be equialteral and establishing the truth <BR>\n" );
document.write( "of the statement cotA + cotB + cotC =sqrt3\r<BR>\n" );
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document.write( "since ABC is equialteral angleA=angleB=angleC=60 degrees\r<BR>\n" );
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document.write( "cotA=cotB=CotC = cot60= 1/sqrt3\r<BR>\n" );
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document.write( "therefore cotA + cotB + cotC = 1/sqrt3 + 1/sqrt3 + 1/sqrt3 <BR>\n" );
document.write( "=3/sqrt3 <BR>\n" );
document.write( "=sqrt3   which is equal to the RHS ( right hand side) of the expression \r<BR>\n" );
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document.write( "hence our assumption that ABC is equilateral is true </SPAN>\n" );
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