document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189940>Question 1189940</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Product to Sum/Sum to Product (TRIGONOMETRY)<BR>\n" );
document.write( "1. Express cos38 + cos106 as a PRODUCT.<BR>\n" );
document.write( "2. Express cos234 cos125 as SUM<BR>\n" );
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document.write( "Thank You! :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821478 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=821478\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Problem 1\r<BR>\n" );
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document.write( "We can use this identity<BR>\n" );
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document.write( "In this case, A = 38 and B = 106\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%2838%29+%2B+cos%28106%29+=+2%2Acos%28+%2838%2B106%29%2F2+%29%2Acos%28+%2838-106%29%2F2+%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=cos%2838%29+%2B+cos%28106%29+=+2%2Acos%28+72+%29%2Acos%28+-34+%29 ALIGN=MIDDLE  ALT=\"cos%2838%29+%2B+cos%28106%29+=+2%2Acos%28+72+%29%2Acos%28+-34+%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=cos%2838%29+%2B+cos%28106%29+=+2%2Acos%28+72+%29%2Acos%28+34+%29 ALIGN=MIDDLE  ALT=\"cos%2838%29+%2B+cos%28106%29+=+2%2Acos%28+72+%29%2Acos%28+34+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Recall that cos(-x) = cos(x).\r<BR>\n" );
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document.write( "<font color=red>Answer:</font> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Acos%28+72+%29%2Acos%28+34+%29 ALIGN=MIDDLE  ALT=\"2%2Acos%28+72+%29%2Acos%28+34+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Problem 2\r<BR>\n" );
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document.write( "We'll use that previous identity, but in reverse.\r<BR>\n" );
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document.write( "We have<BR>\n" );
document.write( "(A+B)/2 = 234<BR>\n" );
document.write( "(A-B)/2 = 125<BR>\n" );
document.write( "as the two arguments in the cosines being multiplied.\r<BR>\n" );
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document.write( "For each equation, multiply both sides by 2<BR>\n" );
document.write( "A+B = 468<BR>\n" );
document.write( "A-B = 250\r<BR>\n" );
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document.write( "Then add straight down<BR>\n" );
document.write( "2A+0B = 718<BR>\n" );
document.write( "2A = 718<BR>\n" );
document.write( "A = 718/2<BR>\n" );
document.write( "A = 359\r<BR>\n" );
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document.write( "This leads to:<BR>\n" );
document.write( "A+B = 468<BR>\n" );
document.write( "359+B = 468<BR>\n" );
document.write( "B = 468-359<BR>\n" );
document.write( "B = 109\r<BR>\n" );
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document.write( "Therefore,<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28+234+%29%2Acos%28+125+%29+=+%281%2F2%29%2A%28cos%28359%29+%2B+cos%28109%29%29 ALIGN=MIDDLE  ALT=\"cos%28+234+%29%2Acos%28+125+%29+=+%281%2F2%29%2A%28cos%28359%29+%2B+cos%28109%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<font color=red>Answer:</font> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2Acos%28359%29+%2B+%281%2F2%29%2Acos%28109%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2Acos%28359%29+%2B+%281%2F2%29%2Acos%28109%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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