document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1114784>Question 1114784</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I verify cot x - tan x = 2 cot 2 x?\r<BR>\n" );
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document.write( "I can get as far as (cos^2 x - sin^2 x)/cos x * sin x.<BR>\n" );
document.write( "I know I need to use a double angle formula here but I don't know how.\r<BR>\n" );
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document.write( "Thanks for your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #729698 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=729698\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot+%28x%29+-+tan+%28x%29+=+2+cot+%282x%29 ALIGN=MIDDLE  ALT=\"cot+%28x%29+-+tan+%28x%29+=+2+cot+%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "first solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot+%282x%29 ALIGN=MIDDLE  ALT=\"cot+%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >using a double angle formula:\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28a%29=cos%28a%29%2Fsin%28a%29 ALIGN=MIDDLE  ALT=\"cot%28a%29=cos%28a%29%2Fsin%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2x ALIGN=MIDDLE  ALT=\"a=2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot+%282x%29=+cos%282x%29%2Fsin%282x%29 ALIGN=MIDDLE  ALT=\"cot+%282x%29=+cos%282x%29%2Fsin%282x%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%282x%29=cos%5E2%28x%29-sin%5E2%28x%29 ALIGN=MIDDLE  ALT=\"cos%282x%29=cos%5E2%28x%29-sin%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282x%29=2sin%28x%29cos%28x%29 ALIGN=MIDDLE  ALT=\"sin%282x%29=2sin%28x%29cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot+%282x%29=+%28cos%5E2%28x%29-sin%5E2%28x%29%29%2F%282sin%28x%29cos%28x%29%29 ALIGN=MIDDLE  ALT=\"cot+%282x%29=+%28cos%5E2%28x%29-sin%5E2%28x%29%29%2F%282sin%28x%29cos%28x%29%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/plot-formula.mpl?expression=cot+%282x%29=+cos%5E2%28x%29%2F%282sin%28x%29cos%28x%29%29+-sin%5E2%28x%29%2F%282sin%28x%29cos%28x%29%29 ALIGN=MIDDLE   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=cot+%282x%29=+cos%28x%29%2F%282sin%28x%29%29+-sin%28x%29%2F%282cos%28x%29%29 ALIGN=MIDDLE  ALT=\"cot+%282x%29=+cos%28x%29%2F%282sin%28x%29%29+-sin%28x%29%2F%282cos%28x%29%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/plot-formula.mpl?expression=cot+%282x%29=cot%28x%29%2F2+-+tan%28x%29%2F2 ALIGN=MIDDLE  ALT=\"cot+%282x%29=cot%28x%29%2F2+-+tan%28x%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then, go back to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot+%28x%29+-+tan+%28x%29+=+2+cot+%282x%29 ALIGN=MIDDLE  ALT=\"cot+%28x%29+-+tan+%28x%29+=+2+cot+%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot+%282x%29=cot%28x%29%2F2+-+tan%28x%29%2F2 ALIGN=MIDDLE  ALT=\"cot+%282x%29=cot%28x%29%2F2+-+tan%28x%29%2F2\"   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=cot+%28x%29+-+tan+%28x%29+=+2+%28cot%28x%29%2F2+-+tan%28x%29%2F2%29 ALIGN=MIDDLE  ALT=\"cot+%28x%29+-+tan+%28x%29+=+2+%28cot%28x%29%2F2+-+tan%28x%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot+%28x%29+-+tan+%28x%29+=+cross%282%29+%28cot%28x%29%2Fcross%282+%29-+tan%28x%29%2Fcross%282%29%29 ALIGN=MIDDLE   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=cot+%28x%29+-+tan+%28x%29+=+cot%28x%29+-+tan%28x%29 ALIGN=MIDDLE  ALT=\"cot+%28x%29+-+tan+%28x%29+=+cot%28x%29+-+tan%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > -> we have proved that left side is equal to right side\r<BR>\n" );
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document.write( " </SPAN>\n" );
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