Fourier transform of cos(x) [closed]

fourier-transform

Use the fact that $\cos(x)=\frac{1}{2}(e^{ix}+e^{-ix})$, and that the Dirac delta function is the Fourier transform of unity:

$$\delta(x)=\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{ikx}dk$$

From here hopefully things will be pretty straightforward.

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