document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155757>Question 1155757</A>: <I><SPAN STYLE=\"word-break: break-all;\"> prove the identity:\r<BR>\n" );
document.write( "\n" );
document.write( "a)   cot((x+pi)/(2)) = -tanx\r<BR>\n" );
document.write( "\n" );
document.write( "b)   tanx = (1 - cos2x)/ (sin2x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #778402 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=778402\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  prove the identity:\r<BR>\n" );
document.write( "\n" );
document.write( "a) It was supposed to be cot(x + pi/2) \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28x%2Bpi%2F2%29+=+-tan%28x%29 ALIGN=MIDDLE  ALT=\"cot%28x%2Bpi%2F2%29+=+-tan%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "manipulate left side\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28+x%2Bpi%2F2%29%2Fsin%28%28x%2Bpi%29%2F2%29 ALIGN=MIDDLE  ALT=\"cos%28+x%2Bpi%2F2%29%2Fsin%28%28x%2Bpi%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .........use identities: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28+x%2Bpi%2F2%29=cos%28x%29%2Acos%28pi%2F2%29+-+sin%28x%29%2Asin%28pi%2F2%29 ALIGN=MIDDLE  ALT=\"cos%28+x%2Bpi%2F2%29=cos%28x%29%2Acos%28pi%2F2%29+-+sin%28x%29%2Asin%28pi%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2Bpi%2F2%29+=sin%28x%29+cos%28pi%2F2%29+%2B+cos%28x%29+sin%28pi%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28x%2Bpi%2F2%29+=sin%28x%29+cos%28pi%2F2%29+%2B+cos%28x%29+sin%28pi%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cos%28x%2F2%29+cos%28pi%2F2%29+-+sin%28x%2F2%29+sin%28pi%2F2%29%29%2F%28sin%28x%2F2%29+cos%28pi%2F2%29+%2B+cos%28x%2F2%29+sin%28pi%2F2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ....since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F2%29=1 ALIGN=MIDDLE  ALT=\"sin%28pi%2F2%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F2%29=0 ALIGN=MIDDLE  ALT=\"cos%28pi%2F2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cos%28x%29+%2A0-+sin%28x%29+%2A1%29%2F%28sin%28x%29+%2A0+%2B+cos%28x%29+%2A1%29+ ALIGN=MIDDLE  ALT=\"%28cos%28x%29+%2A0-+sin%28x%29+%2A1%29%2F%28sin%28x%29+%2A0+%2B+cos%28x%29+%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+sin%28x%29%2Fcos%28x%29+ ALIGN=MIDDLE  ALT=\"-+sin%28x%29%2Fcos%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-tan%28x%29 ALIGN=MIDDLE  ALT=\"+-tan%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28x%2Bpi%2F2%29+=+-tan%28x%29 ALIGN=MIDDLE  ALT=\"cot%28x%2Bpi%2F2%29+=+-tan%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b) \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%29+=+%281+-+cos%282x%29%29%2F+%28sin%282x%29%29 ALIGN=MIDDLE  ALT=\"tan%28x%29+=+%281+-+cos%282x%29%29%2F+%28sin%282x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "manipulate right side:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+-+cos%282x%29%29%2F+%28sin%282x%29%29+ ALIGN=MIDDLE  ALT=\"%281+-+cos%282x%29%29%2F+%28sin%282x%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "use the following identity: \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%282x+%29=1-2sin+%5E2+%28x+%29 ALIGN=MIDDLE  ALT=\"cos+%282x+%29=1-2sin+%5E2+%28x+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282x%29=2cos+%28x%29sin%28x%29 ALIGN=MIDDLE  ALT=\"sin%282x%29=2cos+%28x%29sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+-+%281-2sin%5E2%28x%29%29%29%2F+%282cos%28x%29sin%28x%29%29 ALIGN=MIDDLE  ALT=\"%281+-+%281-2sin%5E2%28x%29%29%29%2F+%282cos%28x%29sin%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+-+1%2B2sin%5E2%28x+%29%29%2F+%282cos%28x%29sin%28x%29%29 ALIGN=MIDDLE  ALT=\"%281+-+1%2B2sin%5E2%28x+%29%29%2F+%282cos%28x%29sin%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sin%5E2%28x%29%2F+%282cos%28x%29sin%28x%29%29 ALIGN=MIDDLE  ALT=\"2sin%5E2%28x%29%2F+%282cos%28x%29sin%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >......simplify\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%282%29sin%5Ecross%282%29%28x%29%2F+%28cross%282%29cos%28x%29cross%28sin%28x%29%29%29 ALIGN=MIDDLE  ALT=\"cross%282%29sin%5Ecross%282%29%28x%29%2F+%28cross%282%29cos%28x%29cross%28sin%28x%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29%2F+cos%28x%29 ALIGN=MIDDLE  ALT=\"sin%28x%29%2F+cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%29 ALIGN=MIDDLE  ALT=\"tan%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );