Chapter 17, Problem 6P

To determine

Prove that the inversion integral reduces to $f\left(t\right)=\frac{1}{2\pi }{\displaystyle {\int }_{-\infty }^{\infty }\left[A\left(\omega \right)\cos \omega t-B\left(\omega \right)\sin \omega t\right]d\omega }$ when $f\left(t\right)$ is a real function of t.