document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=714587>Question 714587</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove the identity:\r<BR>\n" );
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document.write( "(1/1-cosx)-(cosx/1+cosx)=2csc^2(x)-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #438971 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=438971\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Prove the identity: <BR>\n" );
document.write( "(1/1-cosx)-(cosx/1+cosx)=2csc^2(x)-1<BR>\n" );
document.write( "start with left side:<BR>\n" );
document.write( "(1/1-cosx)-(cosx/1+cosx)<BR>\n" );
document.write( "=1+cosx-cosx(1-cosx)/(1-cosx)(1-cosx)<BR>\n" );
document.write( "=1+cosx-cosx+cos^2x/(1-cos^2x)<BR>\n" );
document.write( "=1+cos^2x/(1-cos^2x)<BR>\n" );
document.write( "=(1+1-sin^2x)/1-(1-sin^2x)<BR>\n" );
document.write( "=(2-sin^2x)/sin^2x<BR>\n" );
document.write( "=(2/sin^2x)/(-(sin^2x)/(sin^2x))<BR>\n" );
document.write( "=2csc^2x-1<BR>\n" );
document.write( "verified: left side=right side </SPAN>\n" );
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