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Inverse Trigonometric Functions question

2019 · Shift 2 · Q32

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PYQ Library
JEE Advanced
Mathematics
Inverse Trigonometric Functions
2019 · Shift 2 · Q32

Inverse Trigonometric Functions question

2019 · Shift 2 · Q32

JEE AdvancedMathematicsInverse Trigonometric FunctionsNumerical+3 / −1

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{(k+1)\pi}{2}\right) \right)

in the interval

\left[-\frac{\pi}{4}, \frac{3\pi}{4}\right]

equals ..........

Numerical answer

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