The given angles are sin A =3/5 and tan B= -12/5 where A is an acute angle and B is an obtuse angle.
a. To determine tan A
First find the cos A with the help of trigonometric property
![\cos A=\sqrt[]{1-\sin ^2A}](https://img.qammunity.org/2023/formulas/mathematics/college/ol3vcjzemq9ecy5swdhn25h66zjqnr5u3w.png)
![\cos A=\sqrt[]{1-(9)/(25)}=(4)/(5)](https://img.qammunity.org/2023/formulas/mathematics/college/dwsedqy3tqsf95uj7j1nu86y54hv4jvidq.png)

b. To determine cos(A+B)

We have to find sin B and cosB, it is given that tan B= -12/5



Then the value of cos B is 5/13.
Determine the value of sinB
![\sin B=\sqrt[]{1-(25)/(169)}=(12)/(13)](https://img.qammunity.org/2023/formulas/mathematics/college/lzmj23qzi2tr0ggo7duhbvd38a3ni24lo3.png)
The value of cos (A+B) i