document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=313338>Question 313338</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if tan A = 4/3 and tan B=12/5. find cos (A-B) <BR>\n" );
document.write( "given 0< A < B < pie/2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #224056 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=224056\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Not sure how you're supposed to do this, but:\r<BR>\n" );
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document.write( "tan(A) = 4/3 gets you an angle of 53.13010235 using a calculator.\r<BR>\n" );
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document.write( "tan(B) = 12/5 gets you an angle of 67.38013505 using a calculator.\r<BR>\n" );
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document.write( "Since pi/2 is the same as 180 degrees, then the requirement that 0 < A < B < pi/2 is satisfied.\r<BR>\n" );
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document.write( "A-B = -14.2500327 degrees\r<BR>\n" );
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document.write( "cos(-14.2500327) = .9692307692 using your calculator.\r<BR>\n" );
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document.write( "If you use the cos(A-B) formula, you should get the same answer.\r<BR>\n" );
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document.write( "That formula is cos(A-B) = cos(A)*cos(B) + sin(A)*sin(B)\r<BR>\n" );
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document.write( "Since you have A and B, it's just a matter of plugging the values into the formula.\r<BR>\n" );
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document.write( "You will get cos(A-B) = .969230769 using that formula.\r<BR>\n" );
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document.write( "Once you know the angles, the formula is unnecessary, but this just goes to show you will get the same answer either way.\r<BR>\n" );
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document.write( "Below are the calculations using the cosine(a-b) formula.\r<BR>\n" );
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document.write( "tan(a) = 4/3<BR>\n" );
document.write( "tan(b) = 12/5\r<BR>\n" );
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document.write( "make 2 right triangles, one with angle a and one with angle b.<BR>\n" );
document.write( "use those triangle to solve for the missing side.<BR>\n" );
document.write( "the picture of those triangles is shown below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/may2901.jpg\" alt=\"$$$\" </><BR>\n" );
document.write( "using the pythagorean formula to solve for the missing sides yields.<BR>\n" );
document.write( "sin(a) = 4/5<BR>\n" );
document.write( "cos(a) = 3/5<BR>\n" );
document.write( "sin(b) = 12/13<BR>\n" );
document.write( "cos(b) = 5/13<BR>\n" );
document.write( "now use the cos(a-b) formula to find your answer.<BR>\n" );
document.write( "cos(a-b) = cos(a)cos(b) + sin(a)sin(b)<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "cos(a-b) = 3/5 * 5/13 + 4/5 * 12/13 which becomes:<BR>\n" );
document.write( "15/65 + 48/65 which becomes:<BR>\n" );
document.write( "63/65<BR>\n" );
document.write( "the decimal equivalent of this is .9692307692 which is the same value derived earlier before I knew the correct way to solve this using the sum and difference identity formulas.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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