Question

If n = 1, 2, 3 ..., then cos cos2∝ cos4∝… cos 2n - 1 ∝is equal to

• A. (A) sin⁡2nα2nsin⁡α
• B. (B) sin⁡2nα2nsin⁡2n−1α
• C. (C) sin⁡4n−1α4n−1sin⁡α
• D. (D) sin⁡2nα2nsin⁡α

Answer 1

Answer: (D)

(D) sin⁡2nα2nsin⁡α

Answer 2

Explanation:
Konsider the expression ⇒cos⁡αcos⁡2αcos⁡4α……cos⁡(2n−1)αMultiply and divide the expression by 2nsin⁡α ⇒2n−12nsin⁡α[2sin⁡αcos⁡αcos⁡2αcos⁡4α……cos⁡(2n−1)α]⇒2n−22nsin⁡α[2sin⁡2αcos⁡2αcos⁡4α……cos⁡(2n−1)α]⇒2n−32nsin⁡α[2sin⁡4αcos⁡4α……cos⁡(2n−1)α]⇒12nsin⁡α[2sin⁡2n−1αcos⁡2n−1α]⇒12nsin⁡αsin⁡(2.2n−1α)⇒sin⁡2nα2nsin⁡α