(Solved): Exercise 1: \[ f(t)=[40-20 \sin (2 \pi t+\pi / 6)] \cos (5 \pi t) \] Show that the signal \( f(t) ...

Exercise 1: \[ f(t)=[40-20 \sin (2 \pi t+\pi / 6)] \cos (5 \pi t) \] Show that the signal \( f(t) \) can be represented in the following form, \[ f(t)=a_{1} \cos \left(\omega_{1} t+\theta_{1}\right)+a_{2} \cos \left(\omega_{2} t+\theta_{2}\right)+a_{3} \cos \left(\omega_{3} t+\theta_{3}\right) \] And determine the coefficients \( a_{i}, \omega_{i} \), and \( \theta_{i} \) for \( i=1,2,3 \).