document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=636700>Question 636700</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the minimum value of 4 sec^2 theta + 9 cosec^2 theta ?\r<BR>\n" );
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document.write( "we know the minim value of sec^2 theta is 1. but don't know how to covert the equation completely in to terms of sec^2 theta. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #401195 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=401195\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What is the minimum value of 4 sec^2 theta + 9 cosec^2 theta ? <BR>\n" );
document.write( "we know the minim value of sec^2 theta is 1. but don't know how to covert the equation completely in to terms of sec^2 theta.<BR>\n" );
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document.write( "z = 4sec^2 + 9csc^2<BR>\n" );
document.write( "dz/dx = 4*2*sec*sec*tan + 9*2*csc*(-csc*cot)<BR>\n" );
document.write( "dz/dx = 8sec^2tan - 18csc^2cot = 0<BR>\n" );
document.write( "8sin/cos^3 - 18cos/sin^3 = 0<BR>\n" );
document.write( "8sin^4 - 18cos^4 = 0<BR>\n" );
document.write( "4sin^4 = 9cos^4<BR>\n" );
document.write( "2sin^2 = 3cos^2<BR>\n" );
document.write( "tan^2 = -sqrt(3/2),sqrt(3/2)<BR>\n" );
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document.write( "Find x, then sub into z = 4sec^2 + 9csc^2 to find the minimum, 25<BR>\n" );
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