document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1046271>Question 1046271</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If cos(A-B)+cos(B-C)+cos(C-A)= -3/2, prove that: cosA+cosB+cosC=sinA+sinB+sinC=0. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #662021 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=662021\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consider <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28cosA%2BcosB%2BcosC%29%5E2+%2B+%28sinA%2BsinB%2BsinC%29%5E2+=+cos%5E2%28A%29+%2B+cos%5E2%28B%29+%2B+cos%5E2%28C%29+%2B+2%28cosA%2AcosB+%2B+cosB%2AcosC+%2B+cosA%2AcosC%29+%2B+sin%5E2%28A%29+%2B+sin%5E2%28B%29+%2B+sin%5E2%28C%29+%2B+2%28sinA%2AsinB+%2B+sinB%2AsinC+%2B+sinA%2AsinC%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=1%2B1%2B1+%2B+2%28cosA%2AcosB%2BsinA%2AsinB+%2B+cosB%2AcosC+%2B+sinB%2AsinC+%2B+cosA%2AcosC+%2B+sinA%2AsinC%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=3%2B+2%28cos%28A-B%29+%2B+cos%28B-C%29+%2B+cos%28C-A%29%29 ALIGN=MIDDLE  ALT=\"3%2B+2%28cos%28A-B%29+%2B+cos%28B-C%29+%2B+cos%28C-A%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "But  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28A-B%29%2Bcos%28B-C%29%2Bcos%28C-A%29=+-3%2F2 ALIGN=MIDDLE  ALT=\"cos%28A-B%29%2Bcos%28B-C%29%2Bcos%28C-A%29=+-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B+2%28cos%28A-B%29+%2B+cos%28B-C%29+%2B+cos%28C-A%29%29+=+0 ALIGN=MIDDLE  ALT=\"3%2B+2%28cos%28A-B%29+%2B+cos%28B-C%29+%2B+cos%28C-A%29%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Since the values of A, B, and C are real, all the sine and cosine values are also real, and so, we conclude that \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cosA%2BcosB%2BcosC%29%5E2+=+0 ALIGN=MIDDLE  ALT=\"%28cosA%2BcosB%2BcosC%29%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sinA%2BsinB%2BsinC%29%5E2+=+0 ALIGN=MIDDLE  ALT=\"%28sinA%2BsinB%2BsinC%29%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, hence\r<BR>\n" );
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document.write( "cosA+cosB+cosC = 0  and   sinA+sinB+sinC = 0. </SPAN>\n" );
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