#2**+2 **

cos(u-v)=cos(u)cos(v)+sin(u)sin(v)

given sin(u)=12/13 , cos(v)=-4/5

The given inforamtion is not enough to find the unique answer.

Assume cos(u)=5/13,sin(v)=3/5

cos(u-v)=-4/5*5/13+3/5*12/13=16/65

Assume cos(u)=5/13,sin(v)=-3/5

cos(u-v)=-4/5*5/13+(-3)/5*12/13=-56/65

assmue cos(u)=-5/13,sin(v)=3/5

cos(u-v)=-4/5*(-5)/13+12/13*3/5=56/65

assume cos(u)=-5/13, sin(v)=-3/5

cos(u-v)=-4/5*(-5)/13+12/13*(-3)/5=-16/65

You can find more information in the following link, for this topic read chapter 16

fiora Nov 16, 2018