Explain why the Fourier series of $|\cos(2t)|$ cannot be $\cos(2t)$.

Question

Question: Explain why the Fourier series of $|\cos(2t)|$ cannot be $\cos(2t)$.

I know that $|\cos(2t)|$ is even, so its Fourier series does not have sine term. However, I am not sure why its Fourier series of $|\cos(2t)|$ cannot be $\cos(2t)$.

Answer 1

What a weird question !

Because $|\cos\pi|\ne\cos\pi$.

For completeness, one should add that $|\cos\pi|$ is continuous at $\pi$ so that if it has a Fourier series, it must converge to $|\cos\pi|$.