document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=466502>Question 466502</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To prove:-\r<BR>\n" );
document.write( "\n" );
document.write( "cos12.cos24.cos48.cos84=1/16\r<BR>\n" );
document.write( "\n" );
document.write( "can anyone help me with this................ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #319812 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=319812\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First we should rewrite cos 84 as sin 6 (these two are equal). Denote our desired answer A (which should turn out to be 1/16)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (\sin 6)(\cos 12)(\cos 24)(\cos 48) = A\"> (remember sin 6 is the cos 84)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Suppose we multiply both sides by 16 cos 6:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 16 (\sin 6 )(\cos 6)(\cos 12)( \cos 24 )(\cos 48) = 16 (\cos 6)A\"> \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Applying the double angle identity for sine, we have 2 sin 6 cos 6 = sin 12, and we replace sin 6 cos 6 with (1/2) sin 12 (here I will divide coefficient by 2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 8(\sin 12)(\cos 12)(\cos 24)(\cos 48) = 16 (\cos 6)A\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We apply it again and again:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 4(\sin 24)(\cos 24)(\cos 48) = 16 (\cos 6)A\">\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 48)(\cos 48) = 16(\cos 6)A\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin 96 = 16 (\cos 6)A\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Here, sin 96 is equal to cos 6 (you can verify this either using the sum identity or the unit circle), so we can cancel them out, leaving\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 1 = 16A\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE A = \frac{1}{16}\">, as desired. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );