document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=268428>Question 268428</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove:<BR>\n" );
document.write( "1)sec^2x(1-sin^2x)=1<BR>\n" );
document.write( "2)sinxcosxtanx=1-cos^2x<BR>\n" );
document.write( "3)(cotx/cscx)=cosx<BR>\n" );
document.write( "4)((1-cos^2/tanx))=sinxcosx<BR>\n" );
document.write( "5)(tanx/secx)=sinx\r<BR>\n" );
document.write( "\n" );
document.write( "Can someone please help me by showing me the steps ?? thank you:) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #196703 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=196703\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1)sec^2x(1-sin^2x)=1<BR>\n" );
document.write( "answer - -- ><BR>\n" );
document.write( "Sec(x) = 1/cos(x) <BR>\n" );
document.write( "1-sin^(x) = cos^2(x) so we get<BR>\n" );
document.write( "(1/cos^2(x)) * (cos^2(x))<BR>\n" );
document.write( "which is 1<BR>\n" );
document.write( "1 = 1<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "2)sinxcosxtanx=1-cos^2x<BR>\n" );
document.write( "tan(x) = sin(x)/cos(x) so we get<BR>\n" );
document.write( "sin(x)*cos(x)*sin(x)/cos(x)<BR>\n" );
document.write( "this simplifies to<BR>\n" );
document.write( "sin^2(x)<BR>\n" );
document.write( "this is equal to<BR>\n" );
document.write( "1 - cos^2(x) = 1-cos^2(x)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "3)(cotx/cscx)=cosx<BR>\n" );
document.write( "cot(x) = cos(x) / sin(x)<BR>\n" );
document.write( "csc(x) = 1/sin(x)<BR>\n" );
document.write( "So we  get<BR>\n" );
document.write( "(cos(x) / sin(x)) / (1/sin(x))<BR>\n" );
document.write( "which is<BR>\n" );
document.write( "(cos(x) / sin(x))* (sin(x)/1)<BR>\n" );
document.write( "or simply sin(x) = sin(x)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "4)((1-cos^2/tanx))=sinxcosx<BR>\n" );
document.write( "1-cos^2(x) = sin^2(x) <BR>\n" );
document.write( "tan(x) = sin(x) / cos(x)<BR>\n" );
document.write( "so we get<BR>\n" );
document.write( "(sin^2(x))/(sin(x) / cos(x))<BR>\n" );
document.write( "and then<BR>\n" );
document.write( "(sin^2(x))*(cos(x)/sin(x))<BR>\n" );
document.write( "which is<BR>\n" );
document.write( "sin(x)cos(x) = sin(x)cos(x)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "5)(tanx/secx)=sinx <BR>\n" );
document.write( "tan(x) = sin(x)/cos(x)<BR>\n" );
document.write( "sec(x) = 1/cos(x)<BR>\n" );
document.write( "so we get<BR>\n" );
document.write( "(sin(x)/cos(x))/ (1/cos(x))<BR>\n" );
document.write( "simplify to get<BR>\n" );
document.write( "(sin(x)/cos(x))* cos(x)/1<BR>\n" );
document.write( "or just<BR>\n" );
document.write( "sin(x) = sin(x) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );