document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=360885>Question 360885</A>: <I><SPAN STYLE=\"word-break: break-all;\"> verify the identity cos^4(x)+sin^4(x)=1-(1/2)sin(2x)^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #257483 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20056)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=257483\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Work with the right side only:<BR>\n" );
document.write( "`<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Cos%5E4x%2BSin%5E4x+=+1-expr%281%2F2%29Sin%5E2%282x%29 ALIGN=MIDDLE  ALT=\"Cos%5E4x%2BSin%5E4x+=+1-expr%281%2F2%29Sin%5E2%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "Use the identity: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28Sin%282theta%29=2Sin%28theta%29Cos%28theta%29%29 ALIGN=MIDDLE  ALT=\"red%28Sin%282theta%29=2Sin%28theta%29Cos%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Cos%5E4x%2BSin%5E4x+=+1-expr%281%2F2%29%282Sin%28x%29Cos%28x%29%29%5E2 ALIGN=MIDDLE  ALT=\"Cos%5E4x%2BSin%5E4x+=+1-expr%281%2F2%29%282Sin%28x%29Cos%28x%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "Square the expression in parentheses:<BR>\n" );
document.write( "`<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Cos%5E4x%2BSin%5E4x+=+1-expr%281%2F2%29%282%5E2Sin%5E2x%2ACos%5E2x%29 ALIGN=MIDDLE  ALT=\"Cos%5E4x%2BSin%5E4x+=+1-expr%281%2F2%29%282%5E2Sin%5E2x%2ACos%5E2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "Cancel the 2 into the 2²:<BR>\n" );
document.write( "`<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Cos%5E4x%2BSin%5E4x+=+1-expr%281%2Fcross%282%29%29%282%5Ecross%282%29Sin%5E2x%2ACos%5E2x%29 ALIGN=MIDDLE  ALT=\"Cos%5E4x%2BSin%5E4x+=+1-expr%281%2Fcross%282%29%29%282%5Ecross%282%29Sin%5E2x%2ACos%5E2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Cos%5E4x%2BSin%5E4x+=+1-%282Sin%5E2x%2ACos%5E2x%29 ALIGN=MIDDLE  ALT=\"Cos%5E4x%2BSin%5E4x+=+1-%282Sin%5E2x%2ACos%5E2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "This is a cool trick here. Replace 1 by 1²<BR>\n" );
document.write( "`<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Cos%5E4x%2BSin%5E4x+=+1%5E2-%282Sin%5E2x%2ACos%5E2x%29 ALIGN=MIDDLE  ALT=\"Cos%5E4x%2BSin%5E4x+=+1%5E2-%282Sin%5E2x%2ACos%5E2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "Replace the 1 using the identity: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28Sin%5E2theta+%2B+Cos%5E2theta+=+1%29 ALIGN=MIDDLE  ALT=\"red%28Sin%5E2theta+%2B+Cos%5E2theta+=+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Cos%5E4x%2BSin%5E4x+=+%28Sin%5E2x%2BCos%5E2x%29%5E2-%282Sin%5E2x%2ACos%5E2x%29 ALIGN=MIDDLE  ALT=\"Cos%5E4x%2BSin%5E4x+=+%28Sin%5E2x%2BCos%5E2x%29%5E2-%282Sin%5E2x%2ACos%5E2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "Square out the first term on the right:<BR>\n" );
document.write( "`<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Cos%5E4x%2BSin%5E4x+=+%28Sin%5E4x%2B2Sin%5E2xCos%5E2x%2BCos%5E4x%29-%282Sin%5E2x%2ACos%5E2x%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "Remove the parentheses:<BR>\n" );
document.write( "`<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Cos%5E4x%2BSin%5E4x+=+Sin%5E4x%2B2Sin%5E2xCos%5E2x%2BCos%5E4x-2Sin%5E2x%2ACos%5E2x ALIGN=MIDDLE  ALT=\"Cos%5E4x%2BSin%5E4x+=+Sin%5E4x%2B2Sin%5E2xCos%5E2x%2BCos%5E4x-2Sin%5E2x%2ACos%5E2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "Cancel the terms that cancel:<BR>\n" );
document.write( "`<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Cos%5E4x%2BSin%5E4x+=+Sin%5E4x%2Bcross%282Sin%5E2xCos%5E2x%29%2BCos%5E4x-cross%282Sin%5E2x%2ACos%5E2x%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Cos%5E4x%2BSin%5E4x+=+Sin%5E4x%2BCos%5E4x ALIGN=MIDDLE  ALT=\"Cos%5E4x%2BSin%5E4x+=+Sin%5E4x%2BCos%5E4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "Edwin<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );