document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=643554>Question 643554</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove the identity (1-tanx)^2 + (1- cotx)^2 is equivalent to (secx - cosecx)^2<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #404546 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=404546\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Prove the identity (1-tanx)^2 + (1- cotx)^2 is equivalent to (secx - cosecx)^2<BR>\n" );
document.write( "Identities:<BR>\n" );
document.write( "tan^2+1=sec^2<BR>\n" );
document.write( "cot^2+1=csc^2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Start with left side:<BR>\n" );
document.write( "(1-tanx)^2+(1- cotx)^2<BR>\n" );
document.write( "=(1-2tanx+tan^2x)+(1-2cotx+cot^2x)<BR>\n" );
document.write( "=sec^2x+csc^2x-2(tanx+cotx)<BR>\n" );
document.write( "=sec^2x+csc^2x-2(sinx/cosx+cosx/sinx)<BR>\n" );
document.write( "=sec^2x+csc^2x-2[(sin^2x+cos^2x)/(cosx*sinx)]<BR>\n" );
document.write( "=sec^2x+csc^2x-2[1/(cosx*sinx)]<BR>\n" );
document.write( "=sec^2x+csc^2x-2[(1/cosx)*(1/sinx)]<BR>\n" );
document.write( "=sec^2x+csc^2x-2secx*cscx<BR>\n" );
document.write( "=(secx-cscx)^2<BR>\n" );
document.write( "left side=right side<BR>\n" );
document.write( "given identities are equivalent\r<BR>\n" );
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