Consider an integral equation $$ \frac{1}{z(t)}=f(t)+\alpha\int_0 ^\infty \cos(ts)z(s)\,ds $$
I am required to solve for $z(t)$. I approached this problem by considering the integral on right hand side as cosine transform of $z(t)$. So that the integral equation becomes $$ \frac{1}{z(t)}=f(t)+(2\pi\alpha^2)^{1/2}z(t) $$
We can now solve for $z(t)$. Is this the correct way to solve the problem? If not, can anybody help me solve it?