document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174478>Question 174478</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 84. confirm the identity cos^4x-sin^4x=cos2x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #129465 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=129465\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> cos^4x-sin^4x=cos(2x)... Start with the given equation.\r<BR>\n" );
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document.write( "(cos^2(x))^2-(sin^2(x))^2=cos(2x) ... Factor cos^4x into (cos^2(x))^2. Factor sin^4x into (sin^2(x))^2.\r<BR>\n" );
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document.write( "((1+cos(2x))/2)^2-((1-cos(2x))/2)^2=cos(2x) ... Use the power reducing identities\r<BR>\n" );
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document.write( "((1+cos(2x))/2+(1-cos(2x))/2)((1+cos(2x))/2-(1-cos(2x))/2)=cos(2x) ... Factor the left side using the difference of squares formula\r<BR>\n" );
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document.write( "(2/2)((2cos(2x))/2)=cos(2x) ... Combine the fractions and like terms.\r<BR>\n" );
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document.write( "cos(2x)=cos(2x) ... Reduce. So this verifies the identity<BR>\n" );
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