document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=26174>Question 26174</A>: <I><SPAN STYLE=\"word-break: break-all;\"> verify the identity csc(x)-cot(x)= (2(1-cos(x))(1+cos(x)))/(2sin(x)+sin(2x)) by beginning with the known identity that tan(x/2)=tan(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 #14063 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=14063\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are many ways to verify identities.  One way is to change what you can to sine and cosine expressions.<BR>\n" );
document.write( "Left side work:<BR>\n" );
document.write( "(1/sinx)-(cosx/sinx)=[1-cosx]/sinx<BR>\n" );
document.write( "Right side work:<BR>\n" );
document.write( "[2(1-cosx)(1+cosx)[/[2sinx+2sinx cosx]=2(1-cosx)(1+cosx)/2sinx(1+cosx)<BR>\n" );
document.write( "=(1-cosx)/sinx<BR>\n" );
document.write( "Right side equals left side.  This verifies the identity.\r<BR>\n" );
document.write( "\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );