document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=969333>Question 969333</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please, someone help me with that. Verify algebrically if the equation is an identity. \r<BR>\n" );
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document.write( "Cos(x)/Sec(x)*Sin(x)= Csc(x)- Sin(x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592265 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39626)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=592265\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Equivalent to given:   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Cos%28x%29%2FSec%28x%29%2ASin%28x%29=+Csc%28x%29-+Sin%28x%29 ALIGN=MIDDLE  ALT=\"Cos%28x%29%2FSec%28x%29%2ASin%28x%29=+Csc%28x%29-+Sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Left side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cos%28x%29sin%28x%29%29%2F%281%2Fcos%28x%29%29 ALIGN=MIDDLE  ALT=\"%28cos%28x%29sin%28x%29%29%2F%281%2Fcos%28x%29%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/plot-formula.mpl?expression=cos%28x%29sin%28x%29cos%28x%29 ALIGN=MIDDLE  ALT=\"cos%28x%29sin%28x%29cos%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/plot-formula.mpl?expression=cos%5E2%28x%29sin%28x%29 ALIGN=MIDDLE  ALT=\"cos%5E2%28x%29sin%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/plot-formula.mpl?expression=%281-sin%5E2%28x%29%29sin%28x%29 ALIGN=MIDDLE  ALT=\"%281-sin%5E2%28x%29%29sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a difficult path of steps, so starting new with ....\r<BR>\n" );
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document.write( "The right-hand side:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=csc%28x%29-sin%28x%29 ALIGN=MIDDLE  ALT=\"csc%28x%29-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/plot-formula.mpl?expression=1%2Fsin%28x%29-sin%28x%29 ALIGN=MIDDLE  ALT=\"1%2Fsin%28x%29-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/plot-formula.mpl?expression=1%2Fsin%28x%29-sin%5E2%28x%29%2Fsin%28x%29 ALIGN=MIDDLE  ALT=\"1%2Fsin%28x%29-sin%5E2%28x%29%2Fsin%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/plot-formula.mpl?expression=%281-sin%5E2%28x%29%29%2Fsin%28x%29 ALIGN=MIDDLE  ALT=\"%281-sin%5E2%28x%29%29%2Fsin%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/plot-formula.mpl?expression=cos%5E2%28x%29%2Fsin%28x%29 ALIGN=MIDDLE  ALT=\"cos%5E2%28x%29%2Fsin%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/plot-formula.mpl?expression=cos%28x%29%28cos%28x%29%2Fsin%28x%29%29 ALIGN=MIDDLE  ALT=\"cos%28x%29%28cos%28x%29%2Fsin%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---------Almost resembles the left side, but not fully yet.  We must be able to show that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29%2Fsin%28x%29 ALIGN=MIDDLE  ALT=\"cos%28x%29%2Fsin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is identical to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29%2Fsec%28x%29 ALIGN=MIDDLE  ALT=\"sin%28x%29%2Fsec%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.   Is this a truth?<BR>\n" );
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document.write( "Trying to work with those two smaller or simpler expressions;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29%2Fsec%28x%29 ALIGN=MIDDLE  ALT=\"sin%28x%29%2Fsec%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29%2F%281%2Fcos%28x%29%29 ALIGN=MIDDLE  ALT=\"sin%28x%29%2F%281%2Fcos%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29cos%28x%29 ALIGN=MIDDLE  ALT=\"sin%28x%29cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, NO! Not the same!<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29%2Fsin%28x%29%3C%3Esin%28x%29%2Fsec%28x%29 ALIGN=MIDDLE  ALT=\"cos%28x%29%2Fsin%28x%29%3C%3Esin%28x%29%2Fsec%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Your original equation is NOT an identity. </SPAN>\n" );
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