The maximum value of cosα₁cosα₂·scosαn, with 0≤αi≤ 2 and cotα₁cotα₂·scotαn=1, is (a) 1 2^n/2 (b) 1 2ⁿ (c) 1 2n (d) 1

Correct answer: (a) 1 2^n/2 The constraint Πcotαi=1 with AM–GM forces the maximum at αi= 4, giving ( 1 2 )ⁿ= 1 2^n/2. JEE Advanced 2001 · Trigonometry — verified solution by the Vidaara Team.

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[JEE Advanced 2001] the maximum value of cos alpha 1 cos alpha 2 cos alpha n with

VAVidaara Admin Asked 2d ago 0 views 1 answer

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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 · 2d ago ▲ 0

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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