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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

JEE Main · Mathematics · Trigonometric Ratios & Identities

A 2 A 4 A 2^ n-1 A equals

cos⁡Acos⁡2Acos⁡4A…cos⁡2n−1A\cos A \cos 2 A \cos 4 A \ldots \cos 2^{n-1} A equals

Options

  1. Asin⁡2nA2nsin⁡A\frac{\sin 2^n A}{2^n \sin A}
  2. B2nsin⁡2nAsin⁡A\frac{2^n \sin 2^n A}{\sin A}
  3. C2nsin⁡Asin⁡2nA\frac{2^n \sin A}{\sin 2^n A}
  4. Dsin⁡A2nsin⁡2nA\frac{\sin A}{2^n \sin 2^n A}

Correct answer

A. sin⁡2nA2nsin⁡A\frac{\sin 2^n A}{2^n \sin A}

Step-by-step solution

It is a standard result. cos⁡Acos⁡2Acos⁡22A…cos⁡2n−1A=sin⁡2nA2nsin⁡A\begin{gathered} \cos A \cos 2 A \cos 2^2 A \ldots \cos 2^{n-1} A \\ =\frac{\sin 2^n A}{2^n \sin A} \end{gathered}
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