document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=365339>Question 365339</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a homework problem for trigonometry that is stumping me. it is to verify the identity:\r<BR>\n" );
document.write( "\n" );
document.write( "cot^2x-cos^2x= cot^2xcos^2x. \r<BR>\n" );
document.write( "\n" );
document.write( "I have to make both sides of the equation equal. I have tried using identities such as cot^2x=csc^2x-1, but nothing seems to be working. Thanks for your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #260436 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=260436\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> cot^2x-cos^2x= cot^2xcos^2x  .... Start with the given equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I'm only going to manipulate the right side.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "cot^2x-cos^2x= (csc^2x-1)cos^2x  ... Plug in cot^2x=csc^2x-1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "cot^2x-cos^2x= csc^2xcos^2x-cos^2x  ... Distribute.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "cot^2x-cos^2x= ( 1/(sin^2x) )cos^2x-cos^2x  ... Use the identity csc(x)=1/sin(x).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "cot^2x-cos^2x= (cos^2x)/(sin^2x)-cos^2x  ... Multiply\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "cot^2x-cos^2x= cot^2x-cos^2x  ... Use the identity (cos(x))/(sin(x))=cot(x).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So this verifies the identity. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );