document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=230137>Question 230137</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sinxtanx=secx-cosx </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #170467 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=170467\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your expression is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29+%2A+tan%28x%29 ALIGN=MIDDLE  ALT=\"sin%28x%29+%2A+tan%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%29+=+sin%28x%29+%2F+cos%28x%29 ALIGN=MIDDLE  ALT=\"tan%28x%29+=+sin%28x%29+%2F+cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, your expression becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sin%28x%29+%2A+sin%28x%29%29%2Fcos%28x%29%29 ALIGN=MIDDLE  ALT=\"%28sin%28x%29+%2A+sin%28x%29%29%2Fcos%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29%5E2+%2F+cos%28x%29 ALIGN=MIDDLE  ALT=\"sin%28x%29%5E2+%2F+cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29%5E2+%2B+cos%28x%29%5E2+=+1 ALIGN=MIDDLE  ALT=\"sin%28x%29%5E2+%2B+cos%28x%29%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29%5E2+=+1+-+cos%28x%29%5E2 ALIGN=MIDDLE  ALT=\"sin%28x%29%5E2+=+1+-+cos%28x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29%5E2 ALIGN=MIDDLE  ALT=\"sin%28x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in your expression with this to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+-+cos%28x%29%5E2%29+%2F+cos%28x%29 ALIGN=MIDDLE  ALT=\"%281+-+cos%28x%29%5E2%29+%2F+cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29+=+1%2Fsec%28x%29 ALIGN=MIDDLE  ALT=\"cos%28x%29+=+1%2Fsec%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you can replace cos(x) in your equation to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+-+cos%28x%29%5E2%29+%2F+%281%2Fsec%28x%29%29 ALIGN=MIDDLE  ALT=\"%281+-+cos%28x%29%5E2%29+%2F+%281%2Fsec%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is the same as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+-+cos%28x%29%5E2%29+%2A+%28sec%28x%29%29 ALIGN=MIDDLE  ALT=\"%281+-+cos%28x%29%5E2%29+%2A+%28sec%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F%281%2Fb%29+=+a%2Ab ALIGN=MIDDLE  ALT=\"a%2F%281%2Fb%29+=+a%2Ab\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Your expression has become:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+-+cos%28x%29%5E2%29+%2A+sec%28x%29 ALIGN=MIDDLE  ALT=\"%281+-+cos%28x%29%5E2%29+%2A+sec%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Remove parentheses to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28x%29+-+%28cos%28x%29%5E2+%2A+sec%28x%29%29 ALIGN=MIDDLE  ALT=\"sec%28x%29+-+%28cos%28x%29%5E2+%2A+sec%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28x%29+=+1%2Fcos%28x%29 ALIGN=MIDDLE  ALT=\"sec%28x%29+=+1%2Fcos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you can replace in your equation to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28x%29+-+%28cos%28x%29%5E2%2Fcos%28x%29%29 ALIGN=MIDDLE  ALT=\"sec%28x%29+-+%28cos%28x%29%5E2%2Fcos%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28x%29+-+cos%28x%29 ALIGN=MIDDLE  ALT=\"sec%28x%29+-+cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since this is what you wanted to prove, you're done.\r<BR>\n" );
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document.write( "Note I am showing sin^2(x) as sin(x)^2 because it doesn't come out good on the formula rendering routine with sin^2(x).\r<BR>\n" );
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document.write( "Example:\r<BR>\n" );
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document.write( "sin^2(x) shows up as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "sin(x)^2 shows up as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29%5E2 ALIGN=MIDDLE  ALT=\"sin%28x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The second version is technically incorrect but it shows up clearer so I used it.\r<BR>\n" );
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document.write( "Note that sin(x) * sin(x) really is (sin(x))^2 but I shortened it to sin(x)^2 to eliminate all those extra parentheses that muddied up the presentation.\r<BR>\n" );
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document.write( "Just remember that sin(x)^2 is the same as sin^2(x) and we'll be ok.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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