question_answer

If \[\alpha =22{}^\circ 30',\] then \[(1+\cos \alpha )\,\,(1+\cos \,\,3\alpha )\,\,(1+\cos \,\,5\alpha )\,\,(1+\cos \,\,7\alpha )\]  equal to

A)  \[\frac{1}{8}\] 

B)  \[\frac{1}{4}\]

C)  \[\frac{1+\sqrt{2}}{2\sqrt{2}}\]            

D)  \[\frac{\sqrt{2}-1}{\sqrt{2}+1}\]

E)  None of these