Mark the Correct alternative in the following:

If n = 1, 2, 3, …., then cos α cos 2 α cos 4 α … cos 2^{n – 1} α is equal to

A.

B.

C.

D.

Given expression

cos α cos 2 α cos 4 α … cos 2^{n – 1} α

multiplying and dividing the expression by 2 sin α , we get,

[using sin 2x = 2 sin x cos x]

Now multiplying and dividing the expression with 2.

Continuing this process for n-1 times we will get

Now repeating for the last time,

This proves that

Hence the answer is option D.