document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1145658>Question 1145658</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If tan β = 4/5 then, without a calculator, find tan(𝛑/2 - β). Write your answer as a fraction please.<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 #766912 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=766912\">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( "The formula for the tangent of the difference of two angles, namely:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \tan\(\alpha\,-\,\beta\)\ =\ \frac{\tan\alpha\,-\,\tan\beta}{1\ +\ \tan\alpha\tan\beta}\">\r<BR>\n" );
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document.write( "fails us in this instance because <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \tan\frac{\pi}{2}\"> is undefined.  Pity.\r<BR>\n" );
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document.write( "However, recall that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \tan\varphi\ =\ \frac{\sin\varphi}{\cos\varphi}\">, hence\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \tan\beta\ =\ \frac{4}{5}\ \Rightarrow\ \frac{\sin\beta}{\cos\beta}\ =\ \frac{4}{5}\">\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 \ \ \ \ \ \ \ \ \ \ 5\sin\beta\ =\ 4\cos\beta\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 25\sin^2\beta\ =\ 16\cos^2\beta\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 25\sin^2\beta\ =\ 16\(1\ -\ \sin^2\beta\)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 41\sin^2\beta\ =\ 16\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin\beta\ =\ \pm\frac{4}{\sqrt{41}}\">\r<BR>\n" );
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document.write( "Similarly,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos\beta\ =\ \pm\frac{5}{\sqrt{41}}\">\r<BR>\n" );
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document.write( "Now we can use the difference formulas for sine and cosine to calculate\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin\(\frac{\pi}{2}\,-\,\beta\)\">\r<BR>\n" );
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document.write( "And\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos\(\frac{\pi}{2}\,-\,\beta\)\">\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \tan\beta\ >\ 0\">, the signs of sine and cosine must be the same.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin\(\frac{\pi}{2}\,-\,\beta\)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ =\ 1\,\cdot\,\pm\frac{5}{\sqrt{41}}\ -\ 0\,\cdot\,\pm\frac{4}{\sqrt{41}}\ =\ \pm\frac{5}{\sqrt{41}}\">\r<BR>\n" );
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document.write( "And\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos\(\frac{\pi}{2}\,-\,\beta\)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ =\ 0\,\cdot\,\pm\frac{5}{\sqrt{41}}\ -\ 1\,\cdot\,\pm\frac{4}{\sqrt{41}}\ =\ \pm\frac{4}{\sqrt{41}}\">\r<BR>\n" );
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document.write( "Then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \tan\(\frac{\pi}{2}\,-\,\beta\)\ =\  \frac{\pm\frac{5}{\sqrt{41}}}{\pm\frac{4}{\sqrt{41}}}\ =\ \frac{5}{4}\">\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( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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