document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=855123>Question 855123</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do i prove: \r<BR>\n" );
document.write( "\n" );
document.write( "Cos(x)/sin^2(x)  - cos(x)cot^2(x)=cot(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 #515157 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=515157\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> original equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "cos(x)/sin^2(x) - cos(x)*cot^2(x) = cot(x)*sin(x) <BR>\n" );
document.write( "since cot(x) = cos(x)/sin(x), right side of this equation becomes:<BR>\n" );
document.write( "cos(x)/sin(x)*sin(x) = cos(x)<BR>\n" );
document.write( "your equation becomes:<BR>\n" );
document.write( "cos(x)/sin^2(x) - cos(x)*cot^2(x) = cos(x)<BR>\n" );
document.write( "since cot^2(x) is equal to cos^2(x)/sin^2(x), the left side of your equation becomes:<BR>\n" );
document.write( "cos(x)/sin^2(x) - cos(x)*cos^2(x)/sin^2(x)<BR>\n" );
document.write( "since the denominator are now the same, this expression becomes:<BR>\n" );
document.write( "[cos(x) - cos(x)*cos^2(x)]/sin^2(x)<BR>\n" );
document.write( "factor out the cos(x) in the numerator to get:<BR>\n" );
document.write( "[cos(x)*(1-cos^2(x)]/sin^2(x)<BR>\n" );
document.write( "since 1-cos^2(x) is equal to sin^2(x), this expression becomes:<BR>\n" );
document.write( "[cos(x)*sin^2(x)]/sin^2(x)<BR>\n" );
document.write( "the sin^2(x) in the numerator and the sin^2(x) in the denominator cancel out and you are left with:<BR>\n" );
document.write( "cos(x) on the left side of your equation.<BR>\n" );
document.write( "since cos(x) is on the right side of your equation, the equation becomes:<BR>\n" );
document.write( "cos(x) = cos(x) proving the identity.<BR>\n" );
document.write( "the following piece of paper shos the same calculations done manually which should be easier to follow:<BR>\n" );
document.write( "number 1 shows the original equation to be solved.<BR>\n" );
document.write( "number 2 shows the basic identities that are used in the proof.<BR>\n" );
document.write( "number 3 replaces cot^2(x) with cos^2(x)/sin^2(x) and replaces cot(x) with cos(x)/sin(x)<BR>\n" );
document.write( "number 4 simplifies the equation in number 3.<BR>\n" );
document.write( "number 5 factors out cos(x) that is common to the 2 terms in the numerator or the expression on the left side of the equation.<BR>\n" );
document.write( "number 6 simplifies the equation from number 5.<BR>\n" );
document.write( "number 7 shows the final result which proves the identity is true.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/mar211.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );