# Fourier transform for cosine function

• I
Soumitra
Fourier Transform problem with f(t)=cos(at) for |t|<1 and same f(t)=0 for |t|>1. I have an answer with me as F(w)=[sin(w-a)/(w-a)]+[sin(w+a)/(w+a)]. But I can't show it.

$$\cos x \equiv \frac{e^{ix} + e^{-ix}}{2} \\ \sin x \equiv \frac{e^{ix} - e^{-ix}}{2i}$$