document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=558191>Question 558191</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Cos 2x + cos x + 1= 0. Solve. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #362971 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=362971\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I presume you mean <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \cos 2x + \cos x + 1 = 0\"> instead of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \cos^2 x + \cos x + 1 = 0\">.\r<BR>\n" );
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document.write( "Using trig identities, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (\cos^2 x - \sin^2 x) + \cos x = -1\">\r<BR>\n" );
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document.write( "Regroup this way:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \cos^2 x + \cos x = -1 + \sin^2 x\">\r<BR>\n" );
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document.write( "Now sin^2 - 1 is equal to -cos^2 x, so we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \cos^2 x + \cos x = -\cos^2 x\">\r<BR>\n" );
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document.write( "If cos x = 0 then x = pi/2, 3pi/2, 5pi/2, etc. Otherwise, we may divide by cos x to obtain\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \cos x + 1 = -\cos x \Rightarrow \cos x = -\frac{1}{2}\">\r<BR>\n" );
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document.write( "We obtain x = 2pi/3, 4pi/3, 8pi/3, 10pi/3, ... or in general\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x = \frac{2\pi}{3} + 2k\pi\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x = \frac{4\pi}{3} + 2k\pi\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x = \frac{\pi}{2} + k\pi\"> where k is any integer. </SPAN>\n" );
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