Can you write down the fourier transform as follows? $F(\omega)^2=\left(\int \cos(\omega t) \right)^2 +\left(\int f(t) \sin(\omega t) \right)^2 $

Question

Can you write down the fourier transform as follows?

$$ F(\omega)^2 = \left(\int_{-\infty}^\infty f(t) \cos(\omega t) \right)^2 + \left(\int_{-\infty}^\infty f(t) \sin(\omega t) \right)^2 $$

If so how can you visualise this triangle and why is this true?