document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138018>Question 1138018</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve cos2x = -cosx over the interval 0 ≤ x < 2pi </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #755933 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=755933\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282x%29+=+-cos%28x%29 ALIGN=MIDDLE  ALT=\"cos%282x%29+=+-cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%3C=+x+%3C+2pi ALIGN=MIDDLE  ALT=\"0+%3C=+x+%3C+2pi\"   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=cos+%282x%29%2Bcos+%28x%29+=0 ALIGN=MIDDLE  ALT=\"cos+%282x%29%2Bcos+%28x%29+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........use the following identity : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos++%282x+%29=+-1%2B2+cos%5E2+%28x%29 ALIGN=MIDDLE  ALT=\"cos++%282x+%29=+-1%2B2+cos%5E2+%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/plot-formula.mpl?expression=%28-1%2B2cos%5E2+%28x%29%29%2Bcos+%28x%29+=0 ALIGN=MIDDLE  ALT=\"%28-1%2B2cos%5E2+%28x%29%29%2Bcos+%28x%29+=0\"   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=2cos%5E2+%28x%29+%2Bcos+%28x%29-1+=0 ALIGN=MIDDLE  ALT=\"2cos%5E2+%28x%29+%2Bcos+%28x%29-1+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%28x%29+=u ALIGN=MIDDLE  ALT=\"cos+%28x%29+=u\"   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=2u%5E2++%2Bu-1+=0 ALIGN=MIDDLE  ALT=\"2u%5E2++%2Bu-1+=0\"   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=2u%5E2+-u+%2B2u-1+=0 ALIGN=MIDDLE  ALT=\"2u%5E2+-u+%2B2u-1+=0\"   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=%282u%5E2+-u+%29%2B%282u-1%29+=0 ALIGN=MIDDLE  ALT=\"%282u%5E2+-u+%29%2B%282u-1%29+=0\"   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=u%282u+-1+%29%2B%282u-1%29+=0 ALIGN=MIDDLE  ALT=\"u%282u+-1+%29%2B%282u-1%29+=0\"   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=%28u%2B1%29%282u-1%29+=0 ALIGN=MIDDLE  ALT=\"%28u%2B1%29%282u-1%29+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28u%2B1%29=0 ALIGN=MIDDLE  ALT=\"%28u%2B1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=-1 ALIGN=MIDDLE  ALT=\"u=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282u-1%29+=0 ALIGN=MIDDLE  ALT=\"+%282u-1%29+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=1%2F2 ALIGN=MIDDLE  ALT=\"u=1%2F2\"   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+=u ALIGN=MIDDLE  ALT=\"cos+%28x%29+=u\"   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=cos+%28x%29+=-1 ALIGN=MIDDLE  ALT=\"cos+%28x%29+=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%28x%29+=1%2F2 ALIGN=MIDDLE  ALT=\"cos+%28x%29+=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%28x+%29=-1 ALIGN=MIDDLE  ALT=\"cos+%28x+%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C=x%3C2pi ALIGN=MIDDLE  ALT=\"0%3C=x%3C2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=pi+ ALIGN=MIDDLE  ALT=\"x=pi+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%28x+%29=1%2F2 ALIGN=MIDDLE  ALT=\"cos+%28x+%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0%3C=x%3C2pi ALIGN=MIDDLE  ALT=\"+0%3C=x%3C2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >, than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=pi%2F3 ALIGN=MIDDLE  ALT=\"x=pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5pi%2F3+ ALIGN=MIDDLE  ALT=\"x=5pi%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "combine all solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=pi%2F3 ALIGN=MIDDLE  ALT=\"x=pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5pi%2F3+ ALIGN=MIDDLE  ALT=\"x=5pi%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=pi+ ALIGN=MIDDLE  ALT=\"x=pi+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );