document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=890642>Question 890642</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Verify the following identity by using an angle sum identity: cos (2x)  = 1 – 2(sin2 x).  Hint (2x = x + x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #539196 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=539196\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you want to prove the identity:\r<BR>\n" );
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document.write( "cos(2x) = 1 - 2sin^2(x).\r<BR>\n" );
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document.write( "your basic identity for cos(x + y) is:\r<BR>\n" );
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document.write( "cos(x + y) = cos(x)cos(y) - sin(x)sin(y)\r<BR>\n" );
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document.write( "let y = x, and this basic identity becomes:\r<BR>\n" );
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document.write( "cos(x + x) = cos(x)cos(x) - sin(x)sin(x)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "cos(2x) = cos^2(x) - sin^2(x)\r<BR>\n" );
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document.write( "another basic identity is sin^2(x) + cos^2(x) = 1\r<BR>\n" );
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document.write( "from this basic identity, we can solve for cos^2(x) to get:\r<BR>\n" );
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document.write( "cos^(x) = 1 - sin^2(x).\r<BR>\n" );
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document.write( "replace cos^2(x) with 1 - sin^2(x) in your equation of:\r<BR>\n" );
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document.write( "cos(2x) = cos^2(x) - sin^2(x) to get:\r<BR>\n" );
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document.write( "cos(2x) = 1 - sin^2(x) - sin^2(x)\r<BR>\n" );
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document.write( "simplify this to get:\r<BR>\n" );
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document.write( "cos(2x) = 1 - 2sin^2(x)\r<BR>\n" );
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document.write( "since that is equal to your original equation, you are done.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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