Mathematics · 2021
JEE Main · 3 August 2021, Shift 2 · Q79
The maximum value of ( cos θ_1) ·( cos θ_2) ·( cos θ_3) · … ·( cos θ_10) under the restrictions 0 <θ_1, θ_2, …, θ_10<(π)/2 and ( cot θ_1) ·( cot θ_2)…
The maximum value of $\displaystyle \left(\cos \theta_1\right) \cdot\left(\cos \theta_2\right) \cdot\left(\cos \theta_3\right) \cdot \ldots \cdot\left(\cos \theta_{10}\right)$ under the restrictions $\displaystyle 0$ $\displaystyle <\theta_1, \theta_2, \ldots, \theta_{10}<\frac{\pi}{2}$ and $\displaystyle \left(\cot \theta_1\right) \cdot\left(\cot \theta_2\right) \cdot \ldots \cdot\left(\cot \theta_{10}\right)=1$ is
Official answer
(4)
$\displaystyle \frac{1}{32}$
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JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.