Question 961976
Find the exact value of cos(x-y) if sinx= 4/5 in Quadrant II and tan y=12/5 in Quadrant III
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sinx=4/5
cosx=-3/5
working with (5-12-13) reference right triangle in quadrant III
siny= -12/13
cosy=-5/13
..
Identity: cos(x+y)=cosxcosy-sinxsiny=-3/5*-5/13-4/5*-12/13=15/65+48/65=63/65
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Check:
sinx=4/5 (Q2)
x=126.86˚
tany=12/5 (Q3)
y=247.38˚
x+y=374.24˚
cos(x+y)=cos(374.24)≈0.9692..
Exact value as computed above=63/65≈0.9692..