cos 35° + cos 85° + cos 155° =

(a) 0

$\cos 35^{\circ}+\cos 85^{\circ}+\cos 155^{\circ}$

$=2 \cos \left(\frac{35^{\circ}+85^{\circ}}{2}\right) \cos \left(\frac{35^{\circ}-85^{\circ}}{2}\right)+\cos 155^{\circ} \quad\left[\because \cos A+\cos B=2 \cos \left(\frac{A+B}{2}\right) \cos \left(\frac{A-B}{2}\right)\right]$

$=2 \cos 60^{\circ} \cos \left(-25^{\circ}\right)+\cos 155^{\circ}$

$=2 \times \frac{1}{2} \cos 25^{\circ}+\cos 155^{\circ}$

$=\cos 25^{\circ}+\cos 155^{\circ}$

$=2 \cos \left(\frac{25^{\circ}+155^{\circ}}{2}\right) \cos \left(\frac{25^{\circ}-155^{\circ}}{2}\right)$

$=2 \cos 90^{\circ} \cos 65^{\circ}$

$=0$