document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=829191>Question 829191</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am asked to multiply, then use fundamental identities to Multiply; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.\r<BR>\n" );
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document.write( "The expression is: (sin x + cos x)(sin x - cos x)\r<BR>\n" );
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document.write( "The following I need to compare it to to see which ONE is not equivalent are:<BR>\n" );
document.write( "1 - 2cos^(2)x<BR>\n" );
document.write( "csc^(2)x - cot^(2)x - 2cos^(2)x<BR>\n" );
document.write( "sin^(2)x - cos^(2)x<BR>\n" );
document.write( "2sin^(2)x - sec^(2)x - tan^(2)x<BR>\n" );
document.write( "1 - 2sin ((pi/2) - x) cos x\r<BR>\n" );
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document.write( "If you could please include the steps you used to get your answer as well would be most helpful for me. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #499701 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=499701\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The expression is: (sin x + cos x)(sin x - cos x)<BR>\n" );
document.write( "Use FOIL to get:<BR>\n" );
document.write( "= sin^2(x)-cos^2(x) <BR>\n" );
document.write( "= (1-cos^2(x)-cos^(x))<BR>\n" );
document.write( "= 1 - 2cos^2(x)<BR>\n" );
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document.write( "The following I need to compare it to to see which ONE is not equivalent are:<BR>\n" );
document.write( "1 - 2cos^(2)x::: yes<BR>\n" );
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document.write( "csc^(2)x - cot^(2)x - 2cos^(2)x:: ?<BR>\n" );
document.write( "=(csc^2(x)-cos^2(x)) - 2cos^2(x)<BR>\n" );
document.write( "= 1 - 2cos^2(x)<BR>\n" );
document.write( "So::: yes<BR>\n" );
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document.write( "sin^(2)x - cos^(2)x::: yes<BR>\n" );
document.write( "2sin^(2)x - sec^(2)x - tan^(2)x:: ?<BR>\n" );
document.write( "= 2sin^2(x)-(sec^2x)-tan^2(x))<BR>\n" );
document.write( "= 2sin^2(x)-1<BR>\n" );
document.write( "So::: no<BR>\n" );
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document.write( "1 - 2sin ((pi/2) - x) cos x::: yes<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( " </SPAN>\n" );
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