document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=997682>Question 997682</A>: <I><SPAN STYLE=\"word-break: break-all;\"> prove 2cot2xcosx=cscx-2sinx\r<BR>\n" );
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document.write( "I tried starting on the left.  My work is<BR>\n" );
document.write( "2(cos2x/sin2x)*cosx=<BR>\n" );
document.write( "2(cos^2(x)-sin^2(x)/2sin(x)cos(x))*cos(x)=<BR>\n" );
document.write( "(cos^2(x)-sin^2(x)/sinxcosx)*cos(x)=<BR>\n" );
document.write( "and that's where I get stuck.  If I multiply by that cos(x) then I come up with<BR>\n" );
document.write( "cos^3(x)-sin^2(x)cos(x)/sinxcosx.  Then cross out the cos(x)?  but that doesn't help me either.  Please help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #615671 by </B><A HREF=/tutors/aboutme.mpl?userid=addingup><B>addingup(3677)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=addingup><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=addingup><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=615671\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Prove 2cot2xcosx=cscx-2sinx<BR>\n" );
document.write( "Rewrite like this:<BR>\n" );
document.write( "(cos(2x)/sin(2x))2cos(x)=? 1/sinx-2sin(x)<BR>\n" );
document.write( "(2cos(x)cos(2x)/sin(2x))=? 1-2sin(x)^2/sin(x)<BR>\n" );
document.write( "cross multiply and you get:<BR>\n" );
document.write( "2cos(x)1-2sin(x)^2sin(x)=? sin(2x)(1-2sin(x)^2)<BR>\n" );
document.write( "2cos(x)sin(x)-4cos(x)sin(x)^3=? sin(2x)(1-2sin(x)^2)<BR>\n" );
document.write( "2cos(x)sin(x)-4cos(x)sin(x)^3=? 2cos(x)sin(x)-4cos(x)sin(x)^3<BR>\n" );
document.write( "True, identity verified<BR>\n" );
document.write( "NOTE: the question mark goes over the equal sign until the identity is proven true or false. </SPAN>\n" );
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