Question: Use the frequency shifting property to show that [ mathscr{F}{cos (beta t) u(t)}=frac{j omega}{beta^{2}-omega^{2}}+frac{pi}{2}[delta(omega-beta)+delta(omega+beta)] ]

Use the frequency shifting property to show that

\[
\mathscr{F}\{\cos (\beta t) u(t)\}=\frac{j \omega}{\beta^{2}-\omega^{2}}+\frac{\pi}{2}[\delta(\omega-\beta)+\delta(\omega+\beta)]
\]

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