Question

Prove that:

cos1° cos2° cos3° ... cos180° = 0

Answer 1

LHS \[ = \cos1^\circ \cos2^\circ \cos3^\circ . . . \cos180^\circ \]

\[ = \cos1^\circ \times \cos2^\circ \times \cos3^\circ \times . . . \times \cos90^\circ \times . . . \cos180^\circ \]

\[ = \cos1^\circ \times \cos2^\circ \times \cos3^\circ \times . . . \times 0 \times . . . \cos180^\circ \]

= 0

= RHS