document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=230151>Question 230151</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help, prove: sin^4x-cos^4x/sin^2x=1-cot^2x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #170469 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=170469\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your equation to solve is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "sin^4(x)-cos^4(x)/sin^2(x)=1-cot^2(x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Multiply both sides of this equation by sin^2(x) to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "sin^4(x)-cos^4(x) = (1-cot^2(x)) * sin^2(x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Remove parentheses on the right side of your equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "sin^4(x)-cos^4(x) = sin^2(x) - (cot^2(x)) * sin^2(x))\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since cot(x) = cos(x) / sin(x), and (cos(x)/sin(x))^2 = cos^2(x)/sin^2(x), your equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "sin^4(x)-cos^4(x) = sin^2(x) - (cos^2(x)/sin^2(x)) * sin^2(x))\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Simplify the right side of your equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "sin^4(x)-cos^4(x) = sin^2(x) - cos^2(x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since sin^4(x) - cos^4(x) = (sin^2(x) + cos^2(x)) * (sin^2(x) - cos^2(x)), your equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(sin^2(x) + cos^2(x)) * (sin^2(x) - cos^2(x)) = sin^2(x) - (cos^2(x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since sin^2(x) + cos^2(x) = 1, your equation becomes: \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "sin^2(x) - cos^2(x) = sin^2(x) - (cos^2(x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since this is what you wanted to prove, you're done.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );