document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=424608>Question 424608</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the exact value of Cos1°*Cos2°*...*Cos45°*Csc46°*...Csc89°<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #295937 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=295937\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note that (cos 1)(cos 2)...(cos 45)(csc 46)..(csc 89) = ((cos 1)(cos 2)...(cos 45))/((sin 46)(sin 47)...(sin 89)). Since sin a = cos (90-a), this expression is equal to ((cos 1)(cos 2)...(cos 45))/((cos 44)(cos 43)...(cos 1)). Everything except the cos 45 cancels out, so our expression is equal to cos 45, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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