document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181682>Question 1181682</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use De Moivre's Theorem to find an expression for cot3(theta).  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814014 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=814014\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> De Moivre's theorem:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cos%28x%29+%2B+i%2Asin%28x%29%29%5En+=+cos%28n%2Ax%29+%2B+i%2Asin%28n%2Ax%29 ALIGN=MIDDLE  ALT=\"%28cos%28x%29+%2B+i%2Asin%28x%29%29%5En+=+cos%28n%2Ax%29+%2B+i%2Asin%28n%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for any real number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and integer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   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=%28cos%28x%29+%2B+i%2Asin%28x%29%29%5E3+=+cos%283%2Ax%29+%2B+i%2Asin%283%2Ax%29 ALIGN=MIDDLE  ALT=\"%28cos%28x%29+%2B+i%2Asin%28x%29%29%5E3+=+cos%283%2Ax%29+%2B+i%2Asin%283%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Expanding the left side of the preceding equation, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cos%5E3%28x%29+-3cosx%2Asin%5E2%28x%29%29+%2B+i%2A%283cos%5E2%28x%29%2Asinx+-+sin%5E3%28x%29%29+=cos%283x%29+%2B+i%2Asin%283x%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > after rearranging and combining like terms.\r<BR>\n" );
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document.write( "===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E3%28x%29+-3cosx%2Asin%5E2%28x%29+=+cos%283x%29 ALIGN=MIDDLE  ALT=\"cos%5E3%28x%29+-3cosx%2Asin%5E2%28x%29+=+cos%283x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3cos%5E2%28x%29%2Asinx+-+sin%5E3%28x%29+=+sin%283x%29 ALIGN=MIDDLE  ALT=\"3cos%5E2%28x%29%2Asinx+-+sin%5E3%28x%29+=+sin%283x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "after equating corresponding real and imaginary parts.\r<BR>\n" );
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document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28cot%283x%29%29+=+cos%283x%29%2Fsin%283x%29+=+highlight%28%28cos%5E3%28x%29+-3cosx%2Asin%5E2%28x%29%29%2F+%28+3cos%5E2%28x%29%2Asinx+-+sin%5E3%28x%29+%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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