Answer:
Tan(u–v) = –304/690
Step-by-step explanation:
Putting in mind that sin(theta) and cos(theta) are both negative in the third quadrant, we can find sin(v) and cos(u).
sin(u) = – 5/13 we have opp = 5 and hyp = 13, we make use of Pythagoras theorem to find adj.
Adj = √(13² – 5²) = √(169 – 25) = √144 = 12
cos(u) = – 12/13, therefore tan(u) = 5/12.
cos(v) = –20/29 we have adj = 20 and hyp = 29, we make use of Pythagoras theorem to find opp.
OPP = √(29² – 20²) = √(841 – 400) = √441 = 21
sin(v) = – 21/29, therefore tan(v) =21/20.
tan(u-v) = [tan(u) - tan(v)]/[1 + tan(u)xtan(v)] = [(5/12) - (21/20)]/[1 + (5/12)X(21/20)] = (–19/30)÷(1+7/16) = (–19/30)÷(23/16) =
–304/690
