document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=382048>Question 382048</A>: <I><SPAN STYLE=\"word-break: break-all;\"> verify: sin4x+2sin2xcos2x+cos4x=tanxcotx </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #270863 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=270863\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I hope you meant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E4+%28x%29 ALIGN=MIDDLE  ALT=\"sin%5E4+%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > instead of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%284x%29 ALIGN=MIDDLE  ALT=\"sin+%284x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. I first thought it was the latter interpretation which is not true for all x, but then noticed that the first interpretation yielded a true identity, which I'll explain below:\r<BR>\n" );
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document.write( "First note that tan x cot x = 1 (given that tan x and cot x are nonzero). The expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E4+%28x%29+%2B+2+sin%5E2+%28x%29+cos%5E2+%28x%29+%2B+cos%5E4+%28x%29 ALIGN=MIDDLE  ALT=\"sin%5E4+%28x%29+%2B+2+sin%5E2+%28x%29+cos%5E2+%28x%29+%2B+cos%5E4+%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to\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+%2B+cos%5E2+%28x%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28sin%5E2+%28x%29+%2B+cos%5E2+%28x%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2+%28x%29+%2B+cos%5E2+%28x%29+=+1 ALIGN=MIDDLE  ALT=\"sin%5E2+%28x%29+%2B+cos%5E2+%28x%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%5E2+=+1 ALIGN=MIDDLE  ALT=\"1%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, both sides are equal to 1, and we are done.\r<BR>\n" );
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document.write( "Next time, I would encourage you to put the caret (\"^\") sign to denote an exponent, to make the question less ambiguous. </SPAN>\n" );
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