Just show that on whatever domain you are working on.

Note,(i) Find a bounded solution to Laplace’s equation in the region r <= 1 which satisfies the boundary condition F (1, µ) = cos^2 µ for 0 <= µ < 2pi.

Let

Do you mean perhaps ?(ii) Find a bounded solution to Laplace’s equation in the region r >= 2 which satisfies the boundary condition F (2, µ) = sin^2 µ for 0 <= µ < 2pi

Note,

Let