document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=702592>Question 702592</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if tan alpha = x + 1 and tan beta = x-1, show that 2cot(alpha- beta) = x^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #433086 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=433086\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if tan alpha = x + 1 and tan beta = x-1, show that 2cot(alpha- beta) = x^2<BR>\n" );
document.write( "**<BR>\n" );
document.write( "A=alpha=x+1<BR>\n" );
document.write( "B=beta=x-1<BR>\n" );
document.write( "..<BR>\n" );
document.write( "2cot(A-B)=x^2<BR>\n" );
document.write( "cot(A-B)=x^2/2<BR>\n" );
document.write( "tan(A-B)=2/x^2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Identity: tan(A-B)<BR>\n" );
document.write( "=(tanA-tanB)/(1+tanA*tanB)<BR>\n" );
document.write( "=(x+1)-(x-1)/[1+(x+1)(x-1)]<BR>\n" );
document.write( "=(x+1-x+1)/1+(x^2-1)=2/x^2<BR>\n" );
document.write( "tan(A-B)=2/x^2<BR>\n" );
document.write( "cot(A-B)=x^2/2<BR>\n" );
document.write( "2cot(A-B)=x^2<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );