Question:
Write the value of $\cos 1^{\circ} \cos 2^{\circ} \cos 3^{\circ}$ $\cos 179^{\circ} \cos 180^{\circ}$
Solution:
Given that: $\cos 1^{\circ} \cos 2^{\circ} \cos 3^{\circ} \ldots \cos 179^{\circ} \cos 180^{\circ}$
$=\cos 1^{\circ} \cos 2^{\circ} \cos 3^{\circ} \ldots \cos 179^{\circ} \cos 180^{\circ}$
$=\cos 1^{\circ} \cos 2^{\prime} \cos 3^{\circ} \ldots \cos 89^{\circ} \cos 90^{\circ} \cos 91^{\circ} \ldots \cos 179^{\circ} \cos 180^{\circ}$ $\left[\cos 90^{\circ}=0\right]$
$=\cos 1^{\circ} \cos 2^{\prime} \cos 3^{\ldots} \ldots \cos 89^{\circ} \times 0 \ldots \cos 179^{\prime} \cos 180^{\circ}$
$=0$
Hence the value of $\cos 1^{\circ} \cos 2^{\circ} \cos 3^{\circ} \ldots \cos 179^{\circ} \cos 180^{\circ}$ is 0