document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202473>Question 1202473</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that (tanx)/(1+tanx)= 1/(1+cotx) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837347 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=837347\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'll keep the left hand side (LHS) the same, while altering the right hand side (RHS)<BR>\n" );
document.write( "The goal is to make the LHS and RHS expressions to be identical to each other.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28tan%28x%29%29%2F%281%2Btan%28x%29%29+=+1%2F%281%2Bcot%28x%29%29 ALIGN=MIDDLE  ALT=\"%28tan%28x%29%29%2F%281%2Btan%28x%29%29+=+1%2F%281%2Bcot%28x%29%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=%28tan%28x%29%29%2F%281%2Btan%28x%29%29+=+1%2F%281%2B1%2Ftan%28x%29%29 ALIGN=MIDDLE  ALT=\"%28tan%28x%29%29%2F%281%2Btan%28x%29%29+=+1%2F%281%2B1%2Ftan%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite cot(x) as 1/tan\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28tan%28x%29%29%2F%281%2Btan%28x%29%29+=+%28%28tan%28x%29%29%2F%28tan%28x%29%29%29%2A%281%2F%281%2B1%2Ftan%28x%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply top and bottom by tan/tan, which is equivalent to 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28tan%28x%29%29%2F%281%2Btan%28x%29%29+=+%28tan%28x%29%29%2F%28tan%28x%29%2A%281%2B1%2Ftan%28x%29%29%29 ALIGN=MIDDLE   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=%28tan%28x%29%29%2F%281%2Btan%28x%29%29+=+%28tan%28x%29%29%2F%28tan%28x%29%2Btan%28x%29%2A%281%2Ftan%28x%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute in the denominator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28tan%28x%29%29%2F%281%2Btan%28x%29%29+=+%28tan%28x%29%29%2F%28tan%28x%29%2B1%29 ALIGN=MIDDLE  ALT=\"%28tan%28x%29%29%2F%281%2Btan%28x%29%29+=+%28tan%28x%29%29%2F%28tan%28x%29%2B1%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=%28tan%28x%29%29%2F%281%2Btan%28x%29%29+=+%28tan%28x%29%29%2F%281%2Btan%28x%29%29 ALIGN=MIDDLE  ALT=\"%28tan%28x%29%29%2F%281%2Btan%28x%29%29+=+%28tan%28x%29%29%2F%281%2Btan%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The identity has been confirmed.\r<BR>\n" );
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document.write( "If you wanted to alter the LHS, then keep the RHS the same. You could divide each piece of the LHS by tan(x) to effectively reverse the process shown above.<BR>\n" );
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