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?