document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1112838>Question 1112838</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify the lefthandside so that LHS=RHS\r<BR>\n" );
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document.write( "2/sin(b) = sin(b)/cos(b)-1 + sin(b)/cos(b)+1\r<BR>\n" );
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document.write( "This is a trig identity and I have no clue how to reach my goal on the left-hand side. <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 #727872 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=727872\">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( "I have to assume that you meant:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{2}{\sin(b)}\ =\ \frac{\sin(b)}{\cos(b)-1}\ +\ \frac{\sin(b)}{\cos(b)\ +\ 1}\">\r<BR>\n" );
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document.write( "because resolving the ambiguities any other way doesn't make any sense.  The problem is that the above equation, while it may have a non-null solution set, is not, under any possible definition of the word, an \"identity\".  An identity is a statement that is true for all possible values of the variable.\r<BR>\n" );
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document.write( "As a counter-example to your assertion that this is an identity let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\ =\ \frac{\pi}{2}\">.  Then:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{2}{\sin(\frac{\pi}{2})}\ =\ \frac{\sin(\frac{\pi}{2})}{\cos(\frac{\pi}{2})-1}\ +\ \frac{\sin(\frac{\pi}{2})}{\cos(\frac{\pi}{2})\ +\ 1}\"> \r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sin(\frac{\pi}{2})\ = 1\"> and  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \cos(\frac{\pi}{2})\ = 0\"> the statement becomes\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{2}{1}\ =\ \frac{1}{0-1}\ +\ \frac{1}{0\ +\ 1}\">\r<BR>\n" );
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document.write( "Which is to say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2\ =\ 0\">\r<BR>\n" );
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document.write( "Buzz! Sorry, wrong answer.  Thank you for playing.\r<BR>\n" );
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document.write( "You also have a big problem if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\ =\ \pi\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\ =\ 0\">, since either one of those values gives you a zero denominator in the RHS.\r<BR>\n" );
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document.write( "So either you wrote the problem incorrectly or your instructor is giving you a trick question.  However, no one should have ever referred to what you wrote as an \"identity\".\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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