posted by Heather .
What is the exact value of tan(s+t) if sin(s+t)=56/65. And cos(s)=5/13 and sin(t)=4/5. Everything is in the first quadrant
draw the triangles and you will see that
tan(s) = 12/5
tan(t) = 4/3
Now just plug in your sum formula:
tan(s+t) = (tan s + tan t)/(1 - tan s * tan t)