Question

\[ \cos1^\circ \cos2^\circ \cos3^\circ \cdots \cos179^\circ \]

\[ \text{is equal to} \]

Solution

Observe that the product contains

\[ \cos90^\circ \]

But

\[ \cos90^\circ=0 \]

Therefore,

\[ \cos1^\circ \cos2^\circ \cos3^\circ \cdots \cos179^\circ=0 \]

Answer

\[ \boxed{0} \]