document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163202>Question 1163202</A>: <I><SPAN STYLE=\"word-break: break-all;\"> simplify the given equation<BR>\n" );
document.write( "suppose that sec(a)=5/4 and tab(b)=-1, where 0<a<pi/2<b<pi. find cos(a+b) </SPAN>\n" );
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document.write( "sec(a) = 5/4 and a in quadrant I means cos(a) = 4/5 and sin(a) = 3/5.  Note this means angle a is a bit less than 45 degrees.<br><BR>\n" );
document.write( "tan(b) = -1 and b in quadrant II means sin(b) = sqrt(2)/2 and cos(b) = -sqrt(2)/2.  This angle is clearly 135 degrees.<br><BR>\n" );
document.write( "Before we do actual calculations, note that the angle a+b is going to be a bit less than 180 degrees, which means cos(a+b) should be close to cos(180) = -1.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28a%2Bb%29+=+cos%28a%29cos%28b%29-sin%28a%29sin%28b%29+=+%284%2F5%29%28-sqrt%282%29%2F2%29-%283%2F5%29%28sqrt%282%29%2F2%29+=+%28-7%2F5%29%28sqrt%282%29%2F2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "To 5 decimal places that is -.98995, which is indeed very close to -1.<br><BR>\n" );
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