document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=888750>Question 888750</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to find all solutions of the equation 4 sec x + 4 tan x=4 in the interval [0, 2pi) algebraically </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #537660 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=537660\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4 sec x + 4 tan x=4<BR>\n" );
document.write( "sec x + tan x = 1<BR>\n" );
document.write( "1/cos + sin/cos = cos/cos<BR>\n" );
document.write( "1 + sin = cos<BR>\n" );
document.write( "1 + sin = sqrt(1 - sin^2)<BR>\n" );
document.write( "sin^2 + 2sin + 1 = 1 - sin^2<BR>\n" );
document.write( "2sin^2 + 2sin = 0<BR>\n" );
document.write( "sin(sin + 1) = 0<BR>\n" );
document.write( "sin = 0 --> x = 0, x = pi<BR>\n" );
document.write( "x = pi --> 4*(-1) + 4*0 = 4 so is extraneous<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "sin = -1 --> x = 3pi/2<BR>\n" );
document.write( "@ x = 3pi/2 both sec and tan are undefined<BR>\n" );
document.write( "=======================<BR>\n" );
document.write( "Only x = 0 works </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );