document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=439286>Question 439286</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that the given statement is an identity.\r<BR>\n" );
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document.write( "1)(tan x - cot x)/ (tan x+cot x) = 2sin^2 x - 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #303547 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=303547\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28tan%28x%29+-cot%28+x%29%29%2F%28tan+x%2Bcot+x%29 ALIGN=MIDDLE  ALT=\"%28tan%28x%29+-cot%28+x%29%29%2F%28tan+x%2Bcot+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=2(sin^2)x\r<BR>\n" );
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document.write( "use identities:\r<BR>\n" );
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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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28x%29+=+cos%28x%29%2F+sin%28x%29 ALIGN=MIDDLE  ALT=\"cot%28x%29+=+cos%28x%29%2F+sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "prove that left side is equal to right side:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28tanx+-cotx%29%2F%28tanx%2Bcot+x%29 ALIGN=MIDDLE  ALT=\"%28tanx+-cotx%29%2F%28tanx%2Bcot+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =2sin^2x -1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sinx%2Fcosx+-cosx%2Fsinx%29%2F%28sinx%2Fcosx%2Bcosx%2Fsinx%29 ALIGN=MIDDLE  ALT=\"%28sinx%2Fcosx+-cosx%2Fsinx%29%2F%28sinx%2Fcosx%2Bcosx%2Fsinx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2sin^2 x - 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sin%5E2%28x%29-+cos%5E2%28x%29%29%2Fsin%28x%29cos%28x%29%29%2F%28%28sin%5E2%28x%29-cos%5E2%28x%29%29%2F%28sin%28x%29cos%28x%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >= 2sin^2 x - 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28sin%5E2%28x%29-+cos%5E2%28x%29%29%2Fcross%28sin%28x%29cos%28x%29%29%29%2F%28%28sin%5E2%28x%29%2Bcos%5E2%28x%29%29%2Fcross%28%28sin%28x%29cos%28x%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >= 2sin^2 x - 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sin%5E2%28x%29-cos%5E2%28x%29%29%2F%28sin%5E2%28x%29%2Bcos%5E2%28x%29%29 ALIGN=MIDDLE  ALT=\"%28sin%5E2%28x%29-cos%5E2%28x%29%29%2F%28sin%5E2%28x%29%2Bcos%5E2%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 2sin^2 x - 1...notice that both nominator and denominator have sin and coc squared\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sin%5E2%28x%29-cos%5E2%28x%29%29%2F1 ALIGN=MIDDLE  ALT=\"%28sin%5E2%28x%29-cos%5E2%28x%29%29%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 2sin^2 x - 1\r<BR>\n" );
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document.write( "replace cos^2x with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-sin%5E2%28x%29 ALIGN=MIDDLE  ALT=\"1-sin%5E2%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=sin%5E2%28x%29-%281-sin%5E2%28x%29%29 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29-%281-sin%5E2%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 2sin^2 x - 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29-1%2Bsin%5E2%28x%29 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29-1%2Bsin%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 2sin^2 x - 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sin%5E2%28x%29-1 ALIGN=MIDDLE  ALT=\"2sin%5E2%28x%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 2sin^2 x - 1 </SPAN>\n" );
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