question_answer

If \[\sin 2\alpha =2\sin \alpha \cdot \cos \alpha \] and \[\sin (360{}^\circ -\alpha )=-sin\alpha \] then  find  the value of \[\cos 40{}^\circ \cdot \cos 80{}^\circ \cdot \cos 160{}^\circ .\]

A)  \[\frac{-1}{2}\]                        

B)  \[\frac{-1}{4}\]

C)  \[\frac{-1}{8}\]

D)  \[\frac{-1}{16}\]

E)  None of these