document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142052>Question 1142052</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove cos 3(theta) = 4 cos^3 (theta) - 3cos (theta)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #762738 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52803)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=762738\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This problem is to be solved in 2 easy steps.\r<BR>\n" );
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document.write( "<U>Step 1</U>\r<BR>\n" );
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document.write( "cos(2a) = cos(a + a) = cos(a)*cos(a) - sin(a)*sin(a) = cos^2(a) - sin^2(a) = cos^2(a) - (1-cos^2(a)) = 2*cos^2(a) - 1.\r\n" );
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document.write( "<U>Step 2</U>\r<BR>\n" );
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document.write( "cos(3a) = cos(2a + a) = cos(2a)*cos(a) - sin(2a)*sin(a) = (2cos^2(a)-1)*cos(a) - (2*sin(a)*cos(a))*sin(a) = \r\n" );
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document.write( "                      = 2*cos^3(a) - cos(a) - 2*sin^2(a)*cos(a) = 2*cos^3(a) - cos(a) - 2*(1-cos^2(a))*cos(a) = \r\n" );
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document.write( "                      = 2*cos^3(a) - cos(a) - 2*cos(a) + 2*cos^2(a) = 4*cos^3(a) - 3*cos(a).\r\n" );
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document.write( "It is what has to be proved.\r<BR>\n" );
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