[JEE Advanced 2001] The maximum value of $\cos\alpha_1\cos\alpha_2\cdots\cos\alpha_n$, with $0\le\alpha_i\le\frac\pi2$ and $\cot\alpha_1\cot\alpha_2\cdots\cot\alpha_n=1$, is
The maximum value of $\cos\alpha_1\cos\alpha_2\cdots\cos\alpha_n$, with $0\le\alpha_i\le\frac\pi2$ and $\cot\alpha_1\cot\alpha_2\cdots\cot\alpha_n=1$, is
(a) $\dfrac1{2^{n/2}}$
(b) $\dfrac1{2^n}$
(c) $\dfrac1{2n}$
(d) $1$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 1mo ago
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Correct answer: (a) $\dfrac1{2^{n/2}}$
The constraint $\prod\cot\alpha_i=1$ with AM–GM forces the maximum at $\alpha_i=\frac\pi4$, giving $\left(\frac1{\sqrt2}\right)^n=\frac1{2^{n/2}}$.
JEE Advanced 2001 · Trigonometry — verified solution by the Vidaara Team.
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