document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=860032>Question 860032</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove the following trigonometric identity:\r<BR>\n" );
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document.write( "(sin(x))/(1-cos(x)) + (1-cos(x))/(sin(x)) = 2csc(x)\r<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 #518116 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=518116\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sin%28x%29%29%2F%281-cos%28x%29%29+%2B+%281-cos%28x%29%29%2F%28sin%28x%29%29+=+2csc%28x%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "LHS \r<BR>\n" );
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document.write( "LCM of denominator\r<BR>\n" );
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document.write( "(1-cos(x)(sin(x))\r<BR>\n" );
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document.write( "we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28sin%5E2%28x%29%2B%281-cos%28x%29%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"+%28sin%5E2%28x%29%2B%281-cos%28x%29%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >/<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281-cos%28x%29%29%2A%28sin%28x%29%29%29 ALIGN=MIDDLE  ALT=\"%28%281-cos%28x%29%29%2A%28sin%28x%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(sin^2(x)+1-2cos(x)+cos^2(x))/((1-cos(x)*sin(x))\r<BR>\n" );
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document.write( "(2-2cos(x))/((1-cos(x)*sin(x))\r<BR>\n" );
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document.write( "2(1-cos(x))/(1-cos(x)*sin(x))\r<BR>\n" );
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document.write( "=2/sin(x)\r<BR>\n" );
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document.write( "=2csc (x)\r<BR>\n" );
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document.write( "= RHS </SPAN>\n" );
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