Question

The maximum value of \((\cos \alpha_1) \cdot (\cos \alpha_2) \cdots (\cos \alpha_n)\) under the restrictions \(0 \leq \alpha_1, \alpha_2, \ldots, \alpha_n \leq \frac{\pi}{2}\) and \((\cot \alpha_1) \cdot (\cot \alpha_2) \cdots (\cot \alpha_n) = 1\) is

• A. \(\frac{1}{2^{n/2}}\)
• B. \(\frac{1}{2^n}\)
• C. \(\frac{1}{2n}\)
• D. 1

Hint:

Use \(\cos \alpha \sin \alpha = \frac{1}{2} \sin 2\alpha \leq \frac{1}{2}\).

Answer 1

The Correct Option is A