Pre-Calc HW help about Identities?

Question

find the exact value of the given functions

given Tan (a)= -4/3 in quadrant II and Tan (B)= 12/5 in quadrant III

find
1) sin(a-B)
2) cos(a+B)
3) tan(a-B)

please help me and show your work (: i knwo that the answers are supposed to be in fraction form.
thank you!!!

Answer 1

Tan (a)= -4/3 in quadrant II

sina=4/5

cosa=-3/5

Tan (B)= 12/5 in quadrant III

sinB=-12/13

cosB=-5/13

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Recall trignometric difference formula

sin(a-B)=sinacosB-cosasinB

              =(4/5)(-5/13)-(-3/5)(-12/13)

              =(-20/65)+(36/65)

             =16/65

cos(a+B)=cosacosB-sinasinB

              =(-3/5)(-5/13)-(4/5)(-12/13)

              =(15/65)+(48/65)

             =63/65

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tan(a-B)=tana-tanB/(1+tanatanB)

               =(-4/3)-(12/5)/(1+(-4/3)(12/5))

               =(-20-36)/(15-48)

              =-56/-33

              =56/33