document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=814510>Question 814510</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Proof: sin ^4x -cos^4x=2sin^2 x-1  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #490368 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=490368\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Proof: sin ^4x -cos^4x=2sin^2 x-1<BR>\n" );
document.write( "Start with left side:<BR>\n" );
document.write( "sin^4x-cos^4x=(sin^2x+cos^2x)(sin^2x-cos^2x)(difference of two squares)<BR>\n" );
document.write( "=1*(sin^2x-cos^2x)=sin^2x-(1-sin^2x)=sin^2x-1+sin^2x)<BR>\n" );
document.write( "=2sin^x-1<BR>\n" );
document.write( "verified: left side=right side </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );