Question:
cos 1° cos 2° cos 3° ... cos 180° = ?
(a) 0
(b) 1
(c) –1
(d) $\frac{1}{2}$
Solution:
$\cos 1^{\circ} \cos 2^{\circ} \cos 3^{\circ} \ldots \ldots \cos 180^{\circ}$
$=\cos 1^{\circ} \cos 2^{\circ} \cos 3^{\circ} \ldots \ldots \cos 90^{\circ} \ldots \ldots \cos 180^{\circ}$
$=\cos 1^{\circ} \cos 2^{\circ} \cos 3^{\circ} \ldots \ldots \times 0 \times \ldots \ldots \cos 180^{\circ} \quad\left(\because \cos 90^{\circ}=0\right)$
$=0$
Hence, the correct option is (a).
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