Cosine product series!

$\cos1^\degree\cos2^\degree...\cos89^\degree\red{\cos90^\degree}\cos91^\degree...\cos178^\degree\cos179^\degree=\cos1^\degree\cos2^\degree...\cos89^\degree\times\red{0}\times\cos91^\degree...\cos178^\degree\cos179^\degree=\boxed{0}$

\[\begin{align} \text{Expression} &= \cos{(1^{\circ})} \times \cos{(2^{\circ})} \ldots {\red{\cos{(90^{\circ})}}} \ldots \cos{(179^{\circ})} \times \cos{(180^{\circ})} \\ &= \cos{(1^{\circ})} \times \cos{(2^{\circ})} \ldots {\red{0}} \ldots \cos{(179^{\circ})} \times \cos{(180^{\circ})} \\ &= \boxed{0}

\end{align}\]

Since $\cos 90 = 0$ :

$0 \times x = 0$ , no matter what $x$ is.

Answer: $\fbox 0$