Mathematics · 2022
JEE Main · 27 July 2022, Shift 2 · Q19
Let S={θ ∈(0, (π)/2): Σ_m=1^9 sec (θ+(m-1) (π)/6) sec (θ+(m π)/6)=-8/(√ 3)}. Then
Let $\displaystyle S=\left\{\theta \in\left(0, \frac{\pi}{2}\right): \sum_{m=1}^9 \sec \left(\theta+(m-1) \frac{\pi}{6}\right) \sec \left(\theta+\frac{m \pi}{6}\right)=-\frac{8}{\sqrt{3}}\right\}$. Then
Official answer
(3)
$\displaystyle \sum_{\theta \in S} \theta=\frac{\pi}{2}$
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JEE Main 2022 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.