document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=32478>Question 32478</A>: <I><SPAN STYLE=\"word-break: break-all;\"> prove the following identity:\r<BR>\n" );
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document.write( "cos2A = 2cos^2A - 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #19266 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=19266\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Cos2A = Cos(A+A)\r<BR>\n" );
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document.write( "we know the formula for Cos(A+B)=CosACosB-SinASinB<BR>\n" );
document.write( "therefore Cos(A+A)= CosACosA - SinASinA<BR>\n" );
document.write( "                  = Cos^2A - Sin^2A<BR>\n" );
document.write( "WE also know that Cos^2A + Sin^2A = 1   <BR>\n" );
document.write( "          therfore Sin^2A = 1 - Cos^2A\r<BR>\n" );
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document.write( "Replacing the value of Sin^2A \r<BR>\n" );
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document.write( "Cos(A+A)= Cos^2A - (1 - Cos^2A)<BR>\n" );
document.write( "Cos2A = Cos^2A - 1 +Cos^2A\r<BR>\n" );
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document.write( "Hence Cos2A = 2Cos^2A - 1\r<BR>\n" );
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document.write( "Thus Proved.<BR>\n" );
document.write( " </SPAN>\n" );
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