Question

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

is equal to

(a) \(\frac1{\sqrt2}\)
(b) \(0\)
(c) \(1\)
(d) \(-1\)

Solution

Observe that the product contains

\[ \cos90^\circ \]

But

\[ \cos90^\circ=0 \]

Therefore,

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

Answer

\[ \boxed{0} \]

Correct Option: (b)