(i) Explain how to solve the Fredholm integral equation of the second kind,

$$f(x)=\mu \int_{a}^{b} K(x, t) f(t) d t+g(x)$$

in the case where $K(x, t)$ is of the separable (degenerate) form

$$K(x, t)=a_{1}(x) b_{1}(t)+a_{2}(x) b_{2}(t)$$

(ii) For what values of the real constants $\lambda$ and $A$ does the equation

$$u(x)=\lambda \sin x+A \int_{0}^{\pi}(\cos x \cos t+\cos 2 x \cos 2 t) u(t) d t$$

have (a) a unique solution, (b) no solution?