document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=32482>Question 32482</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove the following identity:\r<BR>\n" );
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document.write( "cos^4theta + 2cos^2theta sin^2theta + sin^4theta = 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #19318 by </B><A HREF=/tutors/aboutme.mpl?userid=sarah_adam><B>sarah_adam(201)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sarah_adam><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=19318\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here iam replacing theta with x<BR>\n" );
document.write( "so your question becomes cos^4x + 2cos^2x sin^2x + sin^4x which can be also written as:<BR>\n" );
document.write( "(cos^2x)^2+2(co^2x)(sin^2x)+ (sin^2x)^2<BR>\n" );
document.write( "If you observe carefully the equation is in the form of a^2+2*a*b+b^2 <BR>\n" );
document.write( "i.e., (a+b)^2<BR>\n" );
document.write( "where a = cos^2x and b = Sin^2x<BR>\n" );
document.write( "therfore the equation can be simplified into (cos^2x +sin^2x)^2<BR>\n" );
document.write( "But we know cos^2x +sin^2x = 1<BR>\n" );
document.write( "therfore (cos^2x +sin^2x)^2 = (1)^2 = 1<BR>\n" );
document.write( "Hence Proved </SPAN>\n" );
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