The value of cos 52° + cos 68° + cos 172° is

(a) 0

$\cos 52^{\circ}+\cos 68^{\circ}+\cos 172^{\circ}$

$=2 \cos \left(\frac{52^{\circ}+68^{\circ}}{2}\right) \cos \left(\frac{52^{\circ}-68^{\circ}}{2}\right)+\cos 172^{\circ} \quad\left[\because \cos A+\cos B=2 \cos \left(\frac{A+B}{2}\right) \cos \left(\frac{A-B}{2}\right)\right]$

$=2 \cos 60^{\circ} \cos \left(-8^{\circ}\right)+\cos 172^{\circ}$

$=2 \times \frac{1}{2} \cos 8^{\circ}+\cos 172^{\circ}$

$=\cos 8^{\circ}+\cos 172^{\circ}$

$=2 \cos \left(\frac{8^{\circ}+172^{\circ}}{2}\right) \cos \left(\frac{8^{\circ}-172^{\circ}}{2}\right)$

$=2 \cos 90^{\circ} \cos 82^{\circ}$

$=0$