Math question on trigonometric identities

So my friend gave me a math question without the answer and I was wondering if the wonderful people from here could help me.

The questions is as follows:
“A and B are obtuse angles such that sin(A)=5/13 and tan(B)=-3/4. Find exact values for sin(A+B), cos(A-B) and tan(A+B).”

I got the answers as sin(A+B)=16/65, cos(A-B)=-33/65 and tan(A+B)=-4/9

Could anyone tell me whether I am right or not, if not could you tell me where I went wrong?