document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=428624>Question 428624</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (1 + cos theta)(1 - cos theta) is that like a difference of squares? So how is it simplified?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #297884 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=297884\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (1 + cos) * (1 - cos) should result in:\r<BR>\n" );
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document.write( "1^2 - cos + cos - cos^2 which should result in 1^2 - cos^2 which should result in 1 - cos^2.\r<BR>\n" );
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document.write( "from the pythagorean theorem, we get sin^2 + cos^2 = 1 (theta, or the angle in question, is implied).\r<BR>\n" );
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document.write( "if we subtract cos^2 from both sides of this equation, we get 1 - cos^2 = sin^2\r<BR>\n" );
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document.write( "so what resulted in 1 - cos^2 should be equivalent to sin^2 which yields to the conclusion that:\r<BR>\n" );
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document.write( "(1 + cos) * (1 - cos) = sin^2\r<BR>\n" );
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document.write( "let's see if this holds water.\r<BR>\n" );
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document.write( "assume our angle is 30 degrees.\r<BR>\n" );
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document.write( "(1 + cos(30)) * (1 - cos(30)) will be equal to .25\r<BR>\n" );
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document.write( "sin (30) = .5\r<BR>\n" );
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document.write( "sin^2 (30) = .5^2 = .25\r<BR>\n" );
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document.write( "looks like it works !!!!!\r<BR>\n" );
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document.write( "let's try another angle at random.\r<BR>\n" );
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document.write( "let's try an angle of 53 degrees\r<BR>\n" );
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document.write( "(1 - cos(53)) * (1 + cos(53) = .637818678\r<BR>\n" );
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document.write( "sin(53) = .79863551\r<BR>\n" );
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document.write( "sin^2(53) = .79863551^2 = .637818678\r<BR>\n" );
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document.write( "it works again !!!!!\r<BR>\n" );
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document.write( "the answer to your question i that, yes, algebraically, this kind of looks like the difference of square, i.e. (x-a) * (x+a) = x^2 - a^2.\r<BR>\n" );
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document.write( "the operation is similar.\r<BR>\n" );
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document.write( "the translation, however, does depend on knowledge of the pythagorean formula of sin^2 + cos^2 = 1 in order to get the final answer.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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