# Write the value of cos 1° cos 2° cos 3° ....... cos 179° cos 180°.

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