question_answer

If \[a=\cos 2\alpha +i\,\,\sin 2\alpha ,\] \[b=\cos \beta +i\,\,\sin 2\beta ,\] \[c=\cos 2\gamma +i\,\,\sin 2\gamma ,\] and \[d=\cos 2\delta +i\,\,\sin 2\delta ,\] then \[\sqrt{abcd}+\frac{1}{\sqrt{abcd}}\] is equal to _________.

A)  \[\cos \,\,(\alpha +\beta +\gamma +\delta )\]

B)  \[2\cos \,\,(\alpha +\beta +\gamma +\delta )\]

C)  \[4\cos \,\,(\alpha +\beta +\gamma +\delta )\]

D)  \[\cos \,\,(\alpha +\beta +\gamma +\delta )+i\,\,sin\,\,(\alpha +\beta +\gamma +\delta )\]

E)  None of these