document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=476614>Question 476614</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the solution of the equation for [0,2pi]\r<BR>\n" );
document.write( "\n" );
document.write( "2(tan(theta))-(sec^2(theta))=0\r<BR>\n" );
document.write( "\n" );
document.write( "Here is what I've done so far:\r<BR>\n" );
document.write( "\n" );
document.write( "2tan(x) = sec^2(x)---> I set them equal because of some rule? and replaced theta w/x to make it easier for me to understand.\r<BR>\n" );
document.write( "\n" );
document.write( "2(sin(x)/cos(x)) = 1/cos(x)\r<BR>\n" );
document.write( "\n" );
document.write( "2 = 1/cos(x) * (cos(x)/sin(x))\r<BR>\n" );
document.write( "\n" );
document.write( "2(cos(x)*sin(x)) = 1<BR>\n" );
document.write( "(cos(x)*sin(x)) = 1/2<BR>\n" );
document.write( "x = ?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #326806 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=326806\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the solution of the equation for [0,2pi]\r<BR>\n" );
document.write( "\n" );
document.write( "2(tan(theta))-(sec^2(theta))=0\r<BR>\n" );
document.write( "\n" );
document.write( "Here is what I've done so far:\r<BR>\n" );
document.write( "\n" );
document.write( "2tan(x) = sec^2(x)---> I set them equal because of some rule? and replaced theta w/x to make it easier for me to understand.\r<BR>\n" );
document.write( "\n" );
document.write( "2(sin(x)/cos(x)) = 1/cos(x)   ****  What happened to the square on the RHS?\r<BR>\n" );
document.write( "\n" );
document.write( "2 = 1/cos(x) * (cos(x)/sin(x))\r<BR>\n" );
document.write( "\n" );
document.write( "2(cos(x)*sin(x)) = 1<BR>\n" );
document.write( "(cos(x)*sin(x)) = 1/2<BR>\n" );
document.write( "x = ?<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "2(tan(theta))-(sec^2(theta))=0<BR>\n" );
document.write( "2sin(x)/cos(x)  - 1/cos^2(x) = 0<BR>\n" );
document.write( "Multiply by cos^2<BR>\n" );
document.write( "2sin(x)cos(x) - 1 = 0<BR>\n" );
document.write( "sin(2x) - 1 = 0<BR>\n" );
document.write( "sin(2x) = 1<BR>\n" );
document.write( "2x = pi/2, 5pi/2<BR>\n" );
document.write( "x = pi/4, 5pi/4<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "You would have gotten it, but you lost the square of the RHS term.<BR>\n" );
document.write( "Then you have to recognize the double angle on the LHS,<BR>\n" );
document.write( "sin(2x) = 2sin(x)cos(x)\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );