JEE (Advanced) 2019 Paper-2 Question 48

Question 48

The value of
$$\sec^{-1} \left(\frac{1}{4}\sum_{k = 0}^{10} \sec \left(\frac{7\pi}{12} + \frac{k\pi}{2}\right) \sec \left(\frac{7\pi}{12} + \frac{\left(k + 1\right)\pi}{2}\right) \right)$$
in the interval $$\begin{bmatrix}-\frac {\pi}{4}, & \frac{3\pi}{4} \end{bmatrix}$$ equals _______


Correct Answer: e



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