document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176263>Question 1176263</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solving identities after factoring out a common function. Determine the missing term.                        ___\r<BR>\n" );
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document.write( "4.sin²x-cos²x / sin x + cos x = sin x-|___|<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #803389 by </B><A HREF=/tutors/aboutme.mpl?userid=Solver92311><B>Solver92311(821)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Solver92311><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=Solver92311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=803389\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\sin^2x\ -\ \cos^2x}{\sin x\ +\ \cos x}\ \equiv\ \sin x\ -\ \varphi(x)\">\r<BR>\n" );
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document.write( "Factor the difference of two squares in the numerator:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\(\sin x\ +\ \cos x\)\(\sin x\ -\ \cos x)}{\sin x\ +\ \cos x}\ \equiv\ \sin x\ -\ \varphi(x)\">\r<BR>\n" );
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document.write( "Eliminate common factors from numerator and denominator:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin x\ -\ cos x\ \equiv\ \sin x\ -\ \varphi(x)\">\r<BR>\n" );
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document.write( "Hence:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \varphi(x)\ =\ \cos x\">\r<BR>\n" );
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document.write( "And the identity is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\sin^2x\ -\ \cos^2x}{\sin x\ +\ \cos x}\ \equiv\ \sin x\ -\ \cos x\">\r<BR>\n" );
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document.write( "Note: You must exclude <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\ =\ \frac{3\pi}{4}\ +\ k\pi\ \forall\ k\ \in\ \mathbb{Z}\"> so that the denominator in the left hand expression is never zero.  Hence, the original expression is not precisely an identity without having made that exclusion in the first place.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> <BR>\n" );
document.write( "I > Ø<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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