document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=836063>Question 836063</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I simply dont understand how to switch from the identites and solve these sort of questions... <BR>\n" );
document.write( "Prove the following identities:<BR>\n" );
document.write( "Tan^4=tan^2thetaxsec^2theta-sec^2theta+1<BR>\n" );
document.write( "1/sectheta+tantheta - 1/sectheta-tantheta = -2 theta<BR>\n" );
document.write( "Sin (90 degrees - theta)-cos^3 theta = costheta x sign^2 theta.\r<BR>\n" );
document.write( "\n" );
document.write( "Please help, 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 #504092 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=504092\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Prove the following identities:<BR>\n" );
document.write( "Tan^4 = tan^2(t)*sec^2(t)-sec^2(t)+1<BR>\n" );
document.write( "Note: 1+tan^2 = sec^2<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Substitute for tan^2 to get:<BR>\n" );
document.write( "(sec^2-1)^2 = (sec^2-1)(sec^2)-(sec^2)+1<BR>\n" );
document.write( "(sec^2-1)^2 = sec^4-2sec^2+1<BR>\n" );
document.write( "Factor the right side::<BR>\n" );
document.write( "(sec^2-1)^2 = (sec^2-1)^2\r<BR>\n" );
document.write( "\n" );
document.write( "----\r<BR>\n" );
document.write( "\n" );
document.write( "1/sec(t)+tan(t) - 1/sec(t)-tan(t) = -2??(t)<BR>\n" );
document.write( "Comment: Some function missing on the right side.<BR>\n" );
document.write( "----------------\r<BR>\n" );
document.write( "\n" );
document.write( "Sin(90 degrees - t)-cos^3(t) = cos(t) x sin^2(t)<BR>\n" );
document.write( "----<BR>\n" );
document.write( "cos(t)-cos^3(t) = cos(t)*sin^2(t)<BR>\n" );
document.write( "cos(t)[1-cos^2(t)] = cos(t)*sin^2(t)<BR>\n" );
document.write( "cos(t)*sin^2(t) = cos(t)(sin^2)t<BR>\n" );
document.write( "===============================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "================ <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );