let tan^-1(u) = A
tan A = u, opposite side, u, adjacent side = 1, hypotenuse = √(u^2+1)
sin A = u/√(u^2+1)
cos A = 1/√(u^2+1)
let tan^-1(v) = B
tan B = v
sin B = v/√(v^2+1)
cos B = 1/√(v^2+1)
cos [ tan^-1(u) + tan^-1(v) ]
= cos(A + B)
= cos A cos B - sin A sin B
= ( 1/√(u^2+1) )(1/√(v^2+1)) - ( u/√(u^2+1) )(v/√(v^2+1))
= ( 1 - uv )/√(u^2+1) )√(v^2+1))
