Chapter 7.12, Problem 25P

(a) Represent as an exponential Fourier transform the function

Hint: Write $\sin x$ in complex exponential form.

(b) Show that your result can be written as $f(x)=\frac{1}{\pi }{\displaystyle {\int }_0^{\infty }\frac{\cos \alpha x+\cos \alpha (x-\pi )}{1-{\alpha }^2}}d\alpha$.