document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167728>Question 167728</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Verify this identity :\r<BR>\n" );
document.write( "\n" );
document.write( "(tan^2(x)-1)/(1+tan^2(x)) = 1-2cos^2(x)\r<BR>\n" );
document.write( "\n" );
document.write( "I've started a couple different options but none are working out for me. Here is what I have so far :\r<BR>\n" );
document.write( "\n" );
document.write( "A)<BR>\n" );
document.write( "multiply top by (1 + tan^2(x)) to get :<BR>\n" );
document.write( "tan^4 (x) -1 or (tan^2(x)+1)(tan^2x-1) <BR>\n" );
document.write( "then i'm stuck!\r<BR>\n" );
document.write( "\n" );
document.write( "B) (tanx +1)(tanx-1)/1 + tan^2(x) =<BR>\n" );
document.write( "(sinx/cosx + 1)(sinx/cosx - 1) / 1/cosx<BR>\n" );
document.write( "then again I'm stuck!\r<BR>\n" );
document.write( "\n" );
document.write( "I'm not sure if I should be working on the right side of the equation instead!  Grrrrr....I could get a little help from the tutors in the Math Lab on campus but we've been instructed not to seek them out for this problem (and another I am stuck on!).  Any tips would be helpful and thank you in advance for your time!!\r<BR>\n" );
document.write( "\n" );
document.write( "Desperately seeking solution, Rebecca<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #677001 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10552)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=677001\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Verify this identity :\r<BR>\n" );
document.write( "\n" );
document.write( "(tan^2(x)-1)/(1+tan^2(x)) = 1-2cos^2(x)\r<BR>\n" );
document.write( "\n" );
document.write( "I've started a couple different options but none are working out for me. Here is what I have so far :\r<BR>\n" );
document.write( "\n" );
document.write( "A)<BR>\n" );
document.write( "multiply top by (1 + tan^2(x)) to get :<BR>\n" );
document.write( "tan^4 (x) -1 or (tan^2(x)+1)(tan^2x-1) <BR>\n" );
document.write( "then i'm stuck!\r<BR>\n" );
document.write( "\n" );
document.write( "B) (tanx +1)(tanx-1)/1 + tan^2(x) =<BR>\n" );
document.write( "(sinx/cosx + 1)(sinx/cosx - 1) / 1/cosx<BR>\n" );
document.write( "then again I'm stuck!\r<BR>\n" );
document.write( "\n" );
document.write( "I'm not sure if I should be working on the right side of the equation instead!  Grrrrr....I could get a little help from the tutors in the Math Lab on campus but we've been instructed not to seek them out for this problem (and another I am stuck on!).  Any tips would be helpful and\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " thank you in advance for your time!!\r<BR>\n" );
document.write( "\n" );
document.write( "Desperately seeking solution, Rebecca<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">It's much, much easier than you think<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28tan%5E2+%28x%29+-+1%29%2F%281+%2B+tan%5E2+%28x%29%29+=+1+-+2cos%5E2+%28x%29 ALIGN=MIDDLE  ALT=\"%28tan%5E2+%28x%29+-+1%29%2F%281+%2B+tan%5E2+%28x%29%29+=+1+-+2cos%5E2+%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<b><u>Left side:</b></u><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sec%5E2+%28x%29+-+1+-+1%29%2F%281+%2B+sec%5E2+%28x%29+-+1%29 ALIGN=MIDDLE  ALT=\"%28sec%5E2+%28x%29+-+1+-+1%29%2F%281+%2B+sec%5E2+%28x%29+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ------ Replacing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C3%2C+tan%5E2+%28x%29%2C+with%2C+sec%5E2+%28x%29%29 ALIGN=MIDDLE  ALT=\"matrix%281%2C3%2C+tan%5E2+%28x%29%2C+with%2C+sec%5E2+%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sec%5E2+%28x%29+-+2%29%2Fsec%5E2+%28x%29 ALIGN=MIDDLE  ALT=\"%28sec%5E2+%28x%29+-+2%29%2Fsec%5E2+%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fcos%5E2+%28x%29+-+2%29%2F%281%2Fcos%5E2+%28x%29%29 ALIGN=MIDDLE  ALT=\"%281%2Fcos%5E2+%28x%29+-+2%29%2F%281%2Fcos%5E2+%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ------ Replacing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C3%2C+sec%5E2+%28x%29%2C+with%2C+1%2Fcos%5E2+%28x%29%29 ALIGN=MIDDLE  ALT=\"matrix%281%2C3%2C+sec%5E2+%28x%29%2C+with%2C+1%2Fcos%5E2+%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fcos%5E2+%28x%29+-+2 ALIGN=MIDDLE  ALT=\"1%2Fcos%5E2+%28x%29+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%F7%22 ALIGN=MIDDLE  ALT=\"%22%F7%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fcos%5E2+%28x%29 ALIGN=MIDDLE  ALT=\"1%2Fcos%5E2+%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ------ Making above LOOK less complex<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+-+2cos%5E2+%28x%29%29%2Fcos%5E2+%28x%29 ALIGN=MIDDLE  ALT=\"%281+-+2cos%5E2+%28x%29%29%2Fcos%5E2+%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%F7%22 ALIGN=MIDDLE  ALT=\"%22%F7%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fcos%5E2+%28x%29 ALIGN=MIDDLE  ALT=\"1%2Fcos%5E2+%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+-+2cos%5E2+%28x%29%29%2Fcos%5E2+%28x%29 ALIGN=MIDDLE  ALT=\"%281+-+2cos%5E2+%28x%29%29%2Fcos%5E2+%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2A%22 ALIGN=MIDDLE  ALT=\"%22%2A%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E2+%28x%29%2F1 ALIGN=MIDDLE  ALT=\"cos%5E2+%28x%29%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- Applying KEEP, CHANGE, FLIP<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+-+2cos%5E2+%28x%29%29%2Fcross%28cos%5E2+%28x%29%29 ALIGN=MIDDLE  ALT=\"%281+-+2cos%5E2+%28x%29%29%2Fcross%28cos%5E2+%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2A%22 ALIGN=MIDDLE  ALT=\"%22%2A%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28cos%5E2+%28x%29%29%2F1 ALIGN=MIDDLE  ALT=\"cross%28cos%5E2+%28x%29%29%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- Canceling numerator and denominator<BR>\n" );
document.write( "<b><u>Left side:</b></u><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%281+-+2cos%5E2+%28x%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%281+-+2cos%5E2+%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, identical to <b><u>Right side:</b></u><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%281+-+2cos%5E2+%28x%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%281+-+2cos%5E2+%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );