Problem reads:

A conducting sphere of radius a is surrounded by a sphere of rdius b having potential
V(θ) = k cosθ.  Find the charge density induced on the surface of the inner sphere.  Take V=0 inside the conducting sphere.

I think that you have to find the potential between the spheres (a < r < b).  Then use the boundary conditions to find σ.  The problem is when you look at the general solution to Laplace's equation between the spheres you can't get rid of the Bl's because the potential will only blow up at the origin, and the origin is not in this region.  So when I evaluate the solution at the surface of the outer sphere the Al's and Bl's are still present. 

Please help any suggestions will be greatly appreciated. Thanks:D