Analytical calculation of the solid angle defined by a cylindrical detector and a point cosine source with parallel axes

We derive analytical expressions for the solid angle subtended by a right finite circular cylinder at a point source with cosine angular distribution in the case where the source direction is parallel to the cylinder axis. As a subsidiary result, an expression for the solid angle subtended by a disc detector at a spread disc source is also provided, in the case where the two discs have a common symmetry axis which is also coincident with the source direction.