document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=199577>Question 199577</A>: <I><SPAN STYLE=\"word-break: break-all;\"> prove this identity (5 marks):\r<BR>\n" );
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document.write( "sin(x) + sin(x)cot(x)^2 = csc(x)\r<BR>\n" );
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document.write( "thanks in advance! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149980 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=149980\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin(x) + \sin(x)\cot^2(x) = \csc(x)\"> ... Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin(x)\left(1 + \cot^2(x)\right) = \csc(x)\"> ... Factor out the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29 ALIGN=MIDDLE  ALT=\"sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin(x)\csc^2(x) = \csc(x)\"> ... Replace the terms in the parenthesis with <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \csc^2(x)\">.\r<BR>\n" );
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document.write( "Note: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 1 + \cot^2(x)=\csc^2(x)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin(x)\left(\frac{1}{\sin^2(x)}\right) = \csc(x)\"> ... Use the identity <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \csc(x)=\frac{1}{\sin(x)}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{\sin(x)}{\sin^2(x)} = \csc(x)\"> ... Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{\sin(x)}{\sin(x)\ast\sin(x)} = \csc(x)\"> ... Factor\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{\sin(x)} = \csc(x)\"> ... Cancel out the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \csc(x) = \csc(x)\"> ... Use the identity <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \csc(x)=\frac{1}{\sin(x)}\">\r<BR>\n" );
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document.write( "So we've proven the identity. </SPAN>\n" );
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