document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=823330>Question 823330</A>: <I><SPAN STYLE=\"word-break: break-all;\"> using cos3x= 4cos^3x -3cosx<BR>\n" );
document.write( "find the general solution for cos3x+2cosx=0\r<BR>\n" );
document.write( "\n" );
document.write( "Soln:<BR>\n" );
document.write( " cos3x+2cosx=0 ............(1)    <BR>\n" );
document.write( "or, 4cos^x-3cosx+2cosx=0       {put the given value of cos3x=4cos^x-3cosx in the                                  <BR>\n" );
document.write( "                                  above equation (1)}<BR>\n" );
document.write( "or, 4cos^3x-cosx=0<BR>\n" );
document.write( "or, cosx(4cos^2x-1)=0<BR>\n" );
document.write( "now we get, cosx=0 and 4cos^2x-1=0<BR>\n" );
document.write( "solve these two equations separately to get the solution.<BR>\n" );
document.write( "taking cosx=0<BR>\n" );
document.write( "or,   cosx=cos90     ,we know the value of cos 90 is zero so put cos90 for 0<BR>\n" );
document.write( "or,     x=90 degree<BR>\n" );
document.write( "now, taking 4cos^2x-1=0<BR>\n" );
document.write( "or,         cos^2x=1/4<BR>\n" );
document.write( "or,          cosx=+1/2 and cosx=-1/2<BR>\n" );
document.write( "or,          cosx=cos60 and cosx=cos120<BR>\n" );
document.write( "or,             x=60 degree and x=120 degree<BR>\n" );
document.write( "hence, the results are x= 90,60,120 degrees. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #495468 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=495468\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> using cos3x= 4cos^3x -3cosx<BR>\n" );
document.write( "find the general solution for <BR>\n" );
document.write( "cos3x+2cosx=0<BR>\n" );
document.write( "interval:[0,2&#960;]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4cos%5E3%28x%29-3cos%28x%29%2B2cos%28x%29=0 ALIGN=MIDDLE  ALT=\"4cos%5E3%28x%29-3cos%28x%29%2B2cos%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4cos%5E3%28x%29-cos%28x%29=0 ALIGN=MIDDLE  ALT=\"4cos%5E3%28x%29-cos%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29%284cos%5E2%28x%29-1%29=0 ALIGN=MIDDLE  ALT=\"cos%28x%29%284cos%5E2%28x%29-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..<BR>\n" );
document.write( "cos(x)=0<BR>\n" );
document.write( "x=&#960;/2,3&#960;/2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "4cos^2(x)-1=0<BR>\n" );
document.write( "cos^2(x)=1/4<BR>\n" );
document.write( "cosx=±&#8730;(1/4)=±1/2<BR>\n" );
document.write( "x=&#960;/3,2&#960;/3,4&#960;/3,5&#960;/3 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );