How is 16cos24cos48cos96cos1681?

Answer 1

The expression (16 \cos 24^\circ \cos 48^\circ \cos 96^\circ \cos 168^\circ) can be simplified using the identity for products of cosines. Specifically, it can be shown that ( \cos x \cos (60^\circ - x) \cos (60^\circ + x) = \frac{1}{4} \cos 3x ). Applying this identity to the angles in the expression leads to the result being equal to 1. Therefore, (16 \cos 24^\circ \cos 48^\circ \cos 96^\circ \cos 168^\circ = 1).