Question 678349
Write sin(cot^-1(u)+ cot^-1(v)) as an algebraic expression containing u and v
-----
Because you want the sin of a sum you need the sin and the cos
of the angles involved.
-------
If the cot is  u/1 find the sin and the cos
sin = 1/sqrt(u^2+1) ; cos = u/sqrt(u^2+1)
--------
If cot is v/1.
sin = 1/sqrt(v^2+1) ; cos = v/sqrt(v^2+1)
-----
Back to Your Problem:
sin(cot^-1(u)+ cot^-1(v)) 

= sin[cot^-1(u)]*cos[cot^-1(v)]
 
+ cos[cot^-1(u)] * sin[cot^-1(v)]
--------------------------

= [1/sqrt(u^2+1)]*[v/sqrt(v^2+1)]
 
+ [u/sqrt(u^2+1)]*[1/sqrt(v^2+1)]
------

The denominators are the same.
----
= [v + u]/[sqrt[(u^2+1)(v^2+1)]
=================================
Cheers,
Stan H.
=================================