document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=532241>Question 532241</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all solutions of each equation on the interval [0, 360)<BR>\n" );
document.write( "Tanx + 1 = Secx\r<BR>\n" );
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document.write( "&#960; = pie<BR>\n" );
document.write( "A.(&#960;/2),(3&#960;/2)<BR>\n" );
document.write( "B. 0<BR>\n" );
document.write( "C.(3&#960;/2)<BR>\n" );
document.write( "D. &#960; </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #350744 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=350744\">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 \ \ \ \ \ \ \ \ \ \ \tan(x)\ +\ 1\ =\ \sec(x)\">\r<BR>\n" );
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document.write( "Use the definitions of tangent and secant:\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)}\ +\ 1\ =\ \frac{1}{\cos(x)}\">\r<BR>\n" );
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document.write( "Add the fractions in the LHS:\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)}{\cos(x)}\ =\ \frac{1}{\cos(x)}\">\r<BR>\n" );
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document.write( "Equate the numerators for the equal denominators:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin(x)\ +\ \cos(x)\ =\ 1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin(x)\ =\ 1\ -\ \cos(x)\">\r<BR>\n" );
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document.write( "Square both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin^2(x)\ =\ 1\ -\ 2\cos(x)\ +\ \cos^2(x)\">\r<BR>\n" );
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document.write( "Pythagorean Identity:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 1\ -\ \cos^2(x)\ =\ 1\ -\ 2\cos(x)\ +\ \cos^2(x)\">\r<BR>\n" );
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document.write( "Collect terms in the LHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2\cos^2(x)\ -\ 2\cos(x)\ =\ 0\">\r<BR>\n" );
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document.write( "Factor\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2\cos(x)\left(\cos(x)\ -\ 1\right)\ =\ 0\">\r<BR>\n" );
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document.write( "So\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos(x)\ =\ 0\">\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos(x)\ =\ 1\">\r<BR>\n" );
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document.write( "But going back to the original equation, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \cos(x)\"> is in the denominator, so discard the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \cos(x)\ =\ 0\"> root.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos(x)\ =\ 1\ \Rightarrow\ x\ =\ \cos^{-1}(1)\ =\ 0\">\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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