document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=35940>Question 35940</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that an isosceles triangle has sides of length a,a, and b and is such that cos(2A)=sin(B). Show that sin^2(B)= -2sin(A)cos(A)cos(B). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #22362 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=22362\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose that an<BR>\n" );
document.write( "isosceles triangle has sides of length a, a, and b and<BR>\n" );
document.write( "is such that cos(2A)=sin(B). Show that<BR>\n" );
document.write( "sin^2(B)=-2sin(A)cos(A)cos(B).<BR>\n" );
document.write( "1 solutions<BR>\n" );
document.write( "Answer 22050 by venugopalramana(1719) About Me  on<BR>\n" );
document.write( "2006-05-03 01:18:38 (Show Source):<BR>\n" );
document.write( "suppose that an isosceles triangle has sides of length<BR>\n" );
document.write( "a, a, and b and is<BR>\n" );
document.write( "> such that cos(2A)=sin(B). Show that<BR>\n" );
document.write( "sin^2(B)=-2sin(A)cos(A)cos(B).<BR>\n" );
document.write( "COS(2A)=SIN(B).............................................................I<BR>\n" );
document.write( "IN A TRIANGLE<BR>\n" );
document.write( "A+B+C=180BUT SINCE C=A<BR>\n" );
document.write( "B+2A=180...................................................................II<BR>\n" );
document.write( "2A=180-B<BR>\n" );
document.write( "COS(2A)=COS(180-B)=-COS(B)....FROM EQN.I,WE GET<BR>\n" );
document.write( "-COS(B)=SIN(B)....OR......COS(B)=-SIN(B)..................................III<BR>\n" );
document.write( "WE HAVE T.S.T.<BR>\n" );
document.write( "SIN^2B=-2SIN(A)COS(A)COS(B),SUBSTITUTING FROM III IN<BR>\n" );
document.write( "RHS<BR>\n" );
document.write( "TST....SIN^2B=-2SIN(A)COS(A)(-SIN(B))....OR.......<BR>\n" );
document.write( "TST....SIN(B)=2SIN(A)COS(A)=SIN(2A)<BR>\n" );
document.write( "USING EQN.II..............2A=180-B.....HENCE<BR>\n" );
document.write( "SIN(2A)=SIN(180-B)=SIN(B)......THUS WE PROVED THE<BR>\n" );
document.write( "RESULT. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );