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

Question

Philoid · Accepted Answer

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.