document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=629319>Question 629319</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please describe two methods that you could use to show that sin(2 + x) = sin 2 + sin x is not an identity. Then use those methods to show that it is not an identity. Thanks!  : ) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #396190 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=396190\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Method 1: Graph the two expressions (the left and right sides). If they produce two distinct graphs, then they are not the same...which means that the equation is not an identity.\r<BR>\n" );
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document.write( "Method 2: Plug in a specific x value that makes the equation false. This is the easiest and most direct way to prove that the equation is not an identity (and sometimes you don't even need a calculator)\r<BR>\n" );
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document.write( "Method 1:\r<BR>\n" );
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document.write( "Graph the left side (in green) and the right side (in blue) using a graphing calculator.\r<BR>\n" );
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document.write( "Clearly the two graphs are different. So the equation sin(2 + x) = sin 2 + sin x is NOT an identity.\r<BR>\n" );
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document.write( "Method 2:\r<BR>\n" );
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document.write( "Plug in any x value (that is NOT a solution to the equation). So let's use the graph to find such a value.\r<BR>\n" );
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document.write( "Let's pick x = 10\r<BR>\n" );
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document.write( "So \r<BR>\n" );
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document.write( "sin(2 + x) = sin(2) + sin(x)\r<BR>\n" );
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document.write( "sin(2 + 10) = sin(2) + sin(10)\r<BR>\n" );
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document.write( "sin(12) = sin(2) + sin(10)\r<BR>\n" );
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document.write( "0.20791169081776 = 0.0348994967025 + 0.17364817766693 ... Note: I'm in degree mode\r<BR>\n" );
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document.write( "0.20791169081776 = 0.20854767436943\r<BR>\n" );
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document.write( "The equation above is not true.\r<BR>\n" );
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document.write( "So the equation is NOT an identity.\r<BR>\n" );
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document.write( "Jim<BR>\n" );
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