hey mate,
cos(A+B) = cos(A)cos(B) - sin(A)sin(B)
Thus,
cos(A+B)/(sin(A)cos(B)) = ( cos(A)cos(B) - sin(A)sin(B) )/ (sin(A) cos(B))
= (cos(A)cos(B))/(sin(A)cos(B)) - (sin(A)sin(B))/(sin(A)cos(B) )
= (cos(A)/sin(A)) - (sin(B)/cos(B))
= cot(A) - tan(B)
So yes its true!
Hope this helps,
David