Question:
The value of $\cos 1^{\circ} \cos 2^{\circ} \cos 3^{\circ}\|.\| \cos 179^{\circ}$ is
(a) $\frac{1}{\sqrt{2}}$
(b) 0
(c) 1
(d) $-1$
Solution:
$\cos 1^{\circ} \cos 2^{\circ} \cos 3^{\circ} \ldots \cos 179^{\circ}$
$=\cos 1^{\circ} \cos 2^{\circ} \cos 3^{\circ} \ldots \cos 90^{\circ} \ldots \cos 179^{\circ}$
$=0 \quad\left(\cos 90^{\circ}=0\right)$
Hence, the correct answer is option B.
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