Given (2ⁿ – 1) x = π

Then evaluate the expression

2ⁿ cos x cos 2x cos2² x ….. cos 2^{n – 1} x

by taking a 2 from 2ⁿ and multiplying and dividing by sin x, we get

[by using the formula sin 2x = 2 sin x cos x]

Now borrowing another 2 from 2^n-1

These iterations repeat till we reach the last term

As already given that

2ⁿ x + x = 180°

2ⁿ x = 180° - x

So substituting the same in the above solution

So the answer is option B.