document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=454166>Question 454166</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find all solutions of the equation tan^2theta=3/2sec theta in the interval [0, 2pi) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #312095 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=312095\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find all solutions of the equation tan^2theta=3/2sec theta in the interval [0, 2pi)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "tan^2x=(3/2)secx<BR>\n" );
document.write( "identity: tan^x+1=sec^2x<BR>\n" );
document.write( "sec^2x-1=3secx/2<BR>\n" );
document.write( "2sec^2x-2=3secx<BR>\n" );
document.write( "2sec^2x-3secx-2=0<BR>\n" );
document.write( "solve by quadratic formula below:<BR>\n" );
document.write( "..<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..<BR>\n" );
document.write( "a=2, b=-3, c=-2\r<BR>\n" );
document.write( "\n" );
document.write( "secx=[-(-3)ħsqrt((-3)^2-4*2*-2)]/2*2<BR>\n" );
document.write( "=[3ħsqrt(9+16)]/4<BR>\n" );
document.write( "=(3ħ&#8730;25)/4<BR>\n" );
document.write( "=(3ħ5)/4<BR>\n" );
document.write( "=8/4=2<BR>\n" );
document.write( "or <BR>\n" );
document.write( "=-2/4=-1/2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "secx=2<BR>\n" );
document.write( "cosx=1/2<BR>\n" );
document.write( "x=&#960;/3 and 5&#960;/3<BR>\n" );
document.write( "or<BR>\n" );
document.write( "secx=-1/2<BR>\n" );
document.write( "cosx=-2 (reject, (-1 < cosx < 1)\r<BR>\n" );
document.write( "\n" );
document.write( "ans: \r<BR>\n" );
document.write( "\n" );
document.write( "x=&#960;/3 and 5&#960;/3 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );