JEE MATHEMATICS MCQ: MULTIPLE AND SUBMULTIPLE ANGLES

1 Hard

1 of 1

Analyzing +4 | -1

The maximum value of

(\cos \,\,{\alpha _1})\;(\cos \,\,{\alpha _2})\,\, \ldots \,\,(\cos \,\,{\alpha _n})\;\;

under the restriction

0\,\, \le \,\,{\alpha _{1,}}{\alpha _2}, \ldots ,{\alpha _n}\,\, \le \,\,\frac{\pi }{2}

and

(\cos \,\,{\alpha _1})\,(\cos \,\,{\alpha _2}) \ldots (\cos \,\,{\alpha _n}) = 1\;\;

, is

View answer and explanation

Correct option: A

\frac{1}{{{2^{n/2}}}}

Option A (

\frac{1}{{{2^{n/2}}}}

) is correct because the maximum value is achieved when all angles are equal, leading to the given result using the AM-GM inequality or similar arguments.

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