document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=608443>Question 608443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to establish the identities:<BR>\n" );
document.write( "(sin(a-b))/(sin(a)cos(b))=1-cot(a)tan(b)\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "2sin(2theta)(1-2sin^2theta)=sin(4theta) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #383195 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=383195\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How to establish the identities:<BR>\n" );
document.write( "(sin(a-b))/(sin(a)cos(b))=1-cot(a)tan(b)<BR>\n" );
document.write( "Use addition formula for sin:  sin(a-b)=sina*cosb-cosa*sinb<BR>\n" );
document.write( "Start with left side:<BR>\n" );
document.write( "(sin(a-b))/(sina*cosb)<BR>\n" );
document.write( "=(sina*cosb-cosa*sinb)/(sina*cosb)<BR>\n" );
document.write( "=1-(cosa*sinb)/(sina*cosb)<BR>\n" );
document.write( "=1-cota*tanb<BR>\n" );
document.write( "verified: left side=right side<BR>\n" );
document.write( "..<BR>\n" );
document.write( "and <BR>\n" );
document.write( "2sin(2theta)(1-2sin^2theta)=sin(4theta)<BR>\n" );
document.write( "use x for theta<BR>\n" );
document.write( "Start with right side:<BR>\n" );
document.write( "sin4x=2sin2xcos2x<BR>\n" );
document.write( "=2sin2x(cos^2x-sin^2x)<BR>\n" );
document.write( "=2sin2x(1-sin2^x-sin^2x)<BR>\n" );
document.write( "=2sin2x(1-2sin^2x)<BR>\n" );
document.write( "verified: right side=left side </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );