$2\cos\large\frac{55^{\large\circ}+65^{\large\circ}}{2}$$\cos\large\frac{55^{\large\circ}-65^{\large\circ}}{2}$$+\cos175^{\large\circ}$
$\Rightarrow 2\cos 60^{\large\circ}\cos(-5)^{\large\circ}+\cos 175^{\large\circ}$
$\Rightarrow 2\times\large\frac{1}{2}.$$\cos 5^{\large\circ}+\cos(180^{\large\circ}-5^{\large\circ})$
$\Rightarrow \cos 5^{\large\circ}-\cos 5^{\large\circ}$
$\Rightarrow 0$
Hence (a) is the correct answer.