document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=575481>Question 575481</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sin^3 3x=(1/2)(sin 3x)(1-cos 6x)\r<BR>\n" );
document.write( "\n" );
document.write( "I need help proving this identity, it is my final problem on my worksheet and I am completely stumped.\r<BR>\n" );
document.write( "\n" );
document.write( "thank you tons!!!!!\r<BR>\n" );
document.write( "\n" );
document.write( "Nicolas </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #369494 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=369494\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now that I have managed to unstump myself...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "First consider the case <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 0\"> in which case the equation reduces to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 0\ =\ 0\">.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Next consider <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ \not =\ 0\">, so <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sin(3x)\ \not =\ 0\"> allowing:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\sin^3(3x)}{\sin(3x)}\ =\ \frac{\frac{1}{2}\left(\sin(3x)\right)\left(1\ -\ \cos(6x)\right)}{\sin(3x)}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "which yields:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin^2(3x)\ =\ \frac{1}{2}\left(1\ -\ \cos(6x)\right)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Still ugly, but an improvement.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE u\ =\ 3x\">, then\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin^2(u)\ =\ \frac{1}{2}\left(1\ -\ \cos(2u)\right)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2\sin^2(u)\ =\ 1\ -\ \cos(2u)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then use <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \cos(2\varphi)\ =\ \cos^2(\varphi)\ -\ \sin^2(\varphi)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to write:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2\sin^2(u)\ =\ 1\ -\ \cos^2(u)\ +\ \sin^2(u)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then use <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin^2(\varphi)\ =\ 1\ -\ \cos^2(\varphi)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to write:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2\sin^2(u)\ =\ \sin^2(u)\ +\ \sin^2(u)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and finally\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2\sin^2(u)\ \equiv\ 2\sin^2(u)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hence\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin^3(3x)\ \equiv\ \frac{1}{2}\left(\sin(3x)\right)\left(1\ -\ \cos(6x)\right)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
document.write( "<div  DISABLED_style= \"text-align:center\"><a  rel=nofollow HREF=\"http://outcampaign.org/\" target=\"_blank\"><IMG STYLE=\"max-width:80%;\" src=\"http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png\" border=\"0\" alt=\"The Out Campaign: Scarlet Letter of Atheism\" width=\"143\" height=\"122\" /></a></div><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );