document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=184174>Question 184174</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Respected Sir,<BR>\n" );
document.write( "I am really amazed to see such a wonderful work on net, which becomes a very useful guide for the students.<BR>\n" );
document.write( "I am having some problem with the subject 'Trigonometry'. Here are the question.<BR>\n" );
document.write( "1) sec^2@-sin^2@.sec^2@=1<BR>\n" );
document.write( "2) (1+2sin^2@)/(1+3tan^2@)=cos^2@<BR>\n" );
document.write( "I hope for a quick reply<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138201 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=138201\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1)  sec^2@-sin^2@.sec^2@=1<BR>\n" );
document.write( "sec^2@(1-sin^2@)=1<BR>\n" );
document.write( "but 1-sin^2@=cos^2@  since sin^2@+cos^2@=1 (fundamental relationship)<BR>\n" );
document.write( "And<BR>\n" );
document.write( "sec^2@=1/cos^2@  since sec@= 1/cos@ (fundamental relationship)<BR>\n" );
document.write( "So<BR>\n" );
document.write( "cos^2@/cos^2@=1<BR>\n" );
document.write( "1=1\r<BR>\n" );
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document.write( "2) (1+2sin^2@)/(1+3tan^2@)=cos^2@<BR>\n" );
document.write( "NUMERATOR:  substitute sin^2@=1-cos^2@ (fundamental relationship) <BR>\n" );
document.write( "(1+2(1-cos^2@))/(1+3tan^2@)=<BR>\n" );
document.write( "(1+2-2cos^2@)/(1+3tan^2@)=<BR>\n" );
document.write( "(3-2cos^2@)/(1+3tan^2@)=<BR>\n" );
document.write( "DENOMINATOR:<BR>\n" );
document.write( "substitute tan^2@=sin^2@/cos^2@ (tan@= sin@/cos@ = fundamental relationship)<BR>\n" );
document.write( "(3-2cos^2@)/(1+3(sin^2@/cos^2@)=<BR>\n" );
document.write( "(3-2cos^2@)/(cos^2@+3sin^2@)/cos^2@)=<BR>\n" );
document.write( "(3-2cos^2@)/(cos^2@+3sin^2@)/cos^2@)=<BR>\n" );
document.write( "substitute sin^2@=1-cos^2@ (fundamental relationship)<BR>\n" );
document.write( "(3-2cos^2@)/(cos^2@+3(1-cos2@)/cos^2@)=<BR>\n" );
document.write( "(3-2cos^2@)/(cos^2@+3-3cos2@)/cos^2@)=<BR>\n" );
document.write( "(3-2cos^2@)/(3-2cos^2@)/cos^2@)=<BR>\n" );
document.write( "FINISH SIMPLIFYING THE FRACTION 3-2cos^2@ in numerator and denominator cancel<BR>\n" );
document.write( "cos^2@(3-2cos^2@)/(3-2cos2@)=cos^2@\r<BR>\n" );
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document.write( "Hope this helps---ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );