document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=217331>Question 217331</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove this identity<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28sin2x+%2B+cos2x+-1%29+%2F+%28sin2x+%2B+cos2x+%2B1%29+ ALIGN=MIDDLE  ALT=\"+%28sin2x+%2B+cos2x+-1%29+%2F+%28sin2x+%2B+cos2x+%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281+-+tanx+%29%2F+%281%2Bcotx%29+ ALIGN=MIDDLE  ALT=\"+%281+-+tanx+%29%2F+%281%2Bcotx%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #163899 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=163899\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Prove this identity\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28sin2x+%2B+cos2x+-1%29+%2F+%28sin2x+%2B+cos2x+%2B1%29+ ALIGN=MIDDLE  ALT=\"+%28sin2x+%2B+cos2x+-1%29+%2F+%28sin2x+%2B+cos2x+%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281+-+tanx+%29%2F+%281%2Bcotx%29+ ALIGN=MIDDLE  ALT=\"+%281+-+tanx+%29%2F+%281%2Bcotx%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 1.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin2x=2cosxsinx ALIGN=MIDDLE  ALT=\"sin2x=2cosxsinx\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos2x=%28cosx%29%5E2-%28sinx%29%5E2=1-2%28sinx%29%5E2 ALIGN=MIDDLE  ALT=\"cos2x=%28cosx%29%5E2-%28sinx%29%5E2=1-2%28sinx%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sin+x%29%5E2%2B%28cos+x%29%5E2=1 ALIGN=MIDDLE  ALT=\"%28sin+x%29%5E2%2B%28cos+x%29%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tanx=sinx%2Fcosx ALIGN=MIDDLE  ALT=\"tanx=sinx%2Fcosx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 2.  Let's work the numerator:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin2x+%2B+cos2x+-1+=++2cosxsinx%2B1-2%28sinx%29%5E2-1 ALIGN=MIDDLE  ALT=\"+sin2x+%2B+cos2x+-1+=++2cosxsinx%2B1-2%28sinx%29%5E2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin2x+%2B+cos2x-1+=+2+cosxsinx-2%28sin+x%29%5E2 ALIGN=MIDDLE  ALT=\"+sin2x+%2B+cos2x-1+=+2+cosxsinx-2%28sin+x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Factor<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%28sin+x%29%5E2 ALIGN=MIDDLE  ALT=\"+2%28sin+x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin2x+%2B+cos2x-1+=+%28cosx%2Fsinx-+1%292%28sin+x%29%5E2 ALIGN=MIDDLE  ALT=\"+sin2x+%2B+cos2x-1+=+%28cosx%2Fsinx-+1%292%28sin+x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin2x%2Bcos2x-1=%28cotx-1%292%28sinx%29%2A2 ALIGN=MIDDLE  ALT=\"+sin2x%2Bcos2x-1=%28cotx-1%292%28sinx%29%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 3.  Let's work with the denominator:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin2x+%2B+cos2x+%2B1 ALIGN=MIDDLE  ALT=\"sin2x+%2B+cos2x+%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin2x+%2B+cos2x+%2B+1+=++2cosxsinx%2B2%28cosx%29%5E2-1%2B1 ALIGN=MIDDLE  ALT=\"+sin2x+%2B+cos2x+%2B+1+=++2cosxsinx%2B2%28cosx%29%5E2-1%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin2x+%2B+cos2x%2B1+=+2+cosxsinx%2B2%28cos+x%29%5E2 ALIGN=MIDDLE  ALT=\"+sin2x+%2B+cos2x%2B1+=+2+cosxsinx%2B2%28cos+x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Factor<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%28cos+x%29%5E2 ALIGN=MIDDLE  ALT=\"+2%28cos+x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin2x+%2B+cos2x%2B1+=+%28sinx%2Fcosx%2B1%292%28cos+x%29%5E2 ALIGN=MIDDLE  ALT=\"+sin2x+%2B+cos2x%2B1+=+%28sinx%2Fcosx%2B1%292%28cos+x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin2x%2Bcos2x%2B1=%28tanx%2B1%292%28cosx%29%5E2 ALIGN=MIDDLE  ALT=\"+sin2x%2Bcos2x%2B1=%28tanx%2B1%292%28cosx%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 4.  Now combine the equations Step 3 and 4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28sin2x+%2B+cos2x+-1%29+%2F+%28sin2x+%2B+cos2x+%2B1%29+ ALIGN=MIDDLE  ALT=\"+%28sin2x+%2B+cos2x+-1%29+%2F+%28sin2x+%2B+cos2x+%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28cotx-1%292%28sinx%29%2A2%29%2F%28tanx%2B1%292%28cosx%29%5E2%29 ALIGN=MIDDLE  ALT=\"%28%28cotx-1%292%28sinx%29%2A2%29%2F%28tanx%2B1%292%28cosx%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sinx%29%5E2%2F%28cox%29%5E2=tanx%2Fcotx ALIGN=MIDDLE  ALT=\"%28sinx%29%5E2%2F%28cox%29%5E2=tanx%2Fcotx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28sin2x+%2B+cos2x+-1%29+%2F+%28sin2x+%2B+cos2x+%2B1%29+ ALIGN=MIDDLE  ALT=\"+%28sin2x+%2B+cos2x+-1%29+%2F+%28sin2x+%2B+cos2x+%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cotx-1%29%2Atanx%2F%28tanx%2B1%29cotx ALIGN=MIDDLE  ALT=\"%28cotx-1%29%2Atanx%2F%28tanx%2B1%29cotx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28sin2x+%2B+cos2x+-1%29+%2F+%28sin2x+%2B+cos2x+%2B1%29+ ALIGN=MIDDLE  ALT=\"+%28sin2x+%2B+cos2x+-1%29+%2F+%28sin2x+%2B+cos2x+%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-tanx%29%2F%281%2Bcotx%29 ALIGN=MIDDLE  ALT=\"%281-tanx%29%2F%281%2Bcotx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 5  ANSWER:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28sin2x+%2B+cos2x+-1%29+%2F+%28sin2x+%2B+cos2x+%2B1%29+ ALIGN=MIDDLE  ALT=\"+%28sin2x+%2B+cos2x+-1%29+%2F+%28sin2x+%2B+cos2x+%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-tanx%29%2F%281%2Bcotx%29 ALIGN=MIDDLE  ALT=\"%281-tanx%29%2F%281%2Bcotx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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