Explanation

(b)
$2\cos{\frac{\pi}{13}\cos{\frac{9\pi}{13} + \cos\frac{3\pi}{13}}} + \cos\frac{5\pi}{13}$
$= 2\cos{\frac{\pi}{13}\cos{\frac{9\pi}{13} + 2\cos{\frac{4\pi}{13}\cos\frac{\pi}{13}}}}$
$= 2\cos{\frac{\pi}{13}\left\lbrack \cos{\frac{9\pi}{13} + \cos\frac{4\pi}{13}} \right\rbrack}$
$= 2\cos{\frac{\pi}{13}\left\lbrack 2\cos{\frac{\pi}{2}.\cos\frac{5\pi}{26}} \right\rbrack}$
$= 0$