A typical question that is found on an (MCQ) exam for a course I'm taking is to express a periodic function in the complex exponential form of the Fourier series
$x(t)=\sum\limits_{k=-\infty}^\infty a_k e^{j\frac{2\pi}{T}kt}$
and we are required to find the coefficients (usually from $a_{-2}$ to $a_2$), where the coefficient $a_k$ is found using:
$a_k=\frac{1}{T}\int_0^Tx(t)e^{-j\frac{2\pi}{T}kt}$
A function that was in a past exam question was:
$x(t)=10+\cos\left(3t+\frac{\pi}{4}\right) + \cos(6t)$
I don't see any way to figure these coefficients out quickly without expanding the trigonometric functions to their exponential form and doing a whole bunch of multiplication; and since this is a fairly short exam I feel like there must be a quicker method/trick to this. How would I quickly find the answer (or at least eliminate incorrect answers?)