document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=199537>Question 199537</A>: <I><SPAN STYLE=\"word-break: break-all;\"> prove this trig identity (5 marks):\r<BR>\n" );
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document.write( "tanx-1 = (sin^2x-cos^2x)/(sinxcosx+cos^2x)\r<BR>\n" );
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document.write( "I've wasted a good 8 pages trying to work this out haha. thanks in advance! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149964 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=149964\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \tan(x)-1=\frac{\sin^2(x)-\cos^2(x)}{\sin(x)\cos(x)+\cos^2(x)}\"> ... Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \tan(x)-1=\frac{\left(\sin(x)+\cos(x)\right) \left( \sin(x)-\cos(x)\right)}{ \sin(x)\cos(x)+\cos^2(x)}\"> ... Factor the numerator using the difference of squares formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \tan(x)-1=\frac{\left(\sin(x)+\cos(x)\right) \left( \sin(x)-\cos(x)\right)}{ \cos(x)\left(\sin(x)+\cos(x)\right)}\"> ... Factor out the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29 ALIGN=MIDDLE  ALT=\"cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the denominator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \tan(x)-1=\frac{\sin(x)-\cos(x)}{\cos(x)}\"> ... Cancel out the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \tan(x)-1=\frac{\sin(x)}{\cos(x)}-\frac{\cos(x)}{\cos(x)}\"> ... Break up the fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \tan(x)-1=\tan(x)-\frac{\cos(x)}{\cos(x)}\"> ... Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29%2Fcos%28x%29 ALIGN=MIDDLE  ALT=\"sin%28x%29%2Fcos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%29 ALIGN=MIDDLE  ALT=\"tan%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \tan(x)-1=\tan(x)-1\"> ... Reduce <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29%2Fcos%28x%29 ALIGN=MIDDLE  ALT=\"cos%28x%29%2Fcos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So this verifies the identity.\r<BR>\n" );
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