Explanation

(b)
$\left( \cos{\frac{10\pi}{13} + \cos\frac{3\pi}{13}} \right) + \left( \cos{\frac{8\pi}{13} +}\cos\frac{5\pi}{13} \right)$
$= 2\cos{\left( \frac{13\pi}{2 \times 13} \right).\cos{\left( \frac{7\pi}{2 \times 13} \right) + 2\cos{\left( \frac{13\pi}{2 \times 13} \right).\cos\left( \frac{3\pi}{2 \times 13} \right)}}}$
$= 2\cos{\frac{\pi}{2}\left( \cos{\frac{7\pi}{26} + \cos\frac{3\pi}{26}} \right)} = 0$