Question

giving that cosx=4/5 and siny=12/13, find cos(x+y) when x is acute and y is obtuse angle

Answer 1

draw two right - angled triangles
you should recognize the first to be the 3-4-5 and the second as the 5-12-13 Pythagorean triangles

if cosx = 4/5, then sinx = 3/5
if siny = 12/13, then cosy = 5/13

cos(x+y) = cosxcosy - sinx siny
= (4/5)(5/13) - (3/5)(12/13)
= 20/65 - 36/65
= -16/65

Answer 2

Did not notice that y was supposed to be an obtuse angle, that would make y an angle in quadrant II and
cosy = -5/13

make the necessary changes