Fourier Transform--Cosine

$\displaystyle {\mathcal F}[\cos(2\pi k_0x)]$	$\textstyle =$	$\displaystyle \int_{-\infty}^\infty e^{-2\pi ikx}\left({e^{2\pi ik_0x}+e^{-2\pi ik_0 x}\over 2}\right)\,dx$
	$\textstyle =$	$\displaystyle {\textstyle{1\over 2}}\int_{-\infty}^\infty [e^{-2\pi i(k-k_0)x}+e^{-2\pi i(k+k_0)x}]\,dx$
	$\textstyle =$	$\displaystyle {\textstyle{1\over 2}}[\delta(k-k_0)+\delta(k+k_0)],$