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Inverse Trigonometric Functions question

2025 · 4 Apr · Shift 2 · Q40

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JEE Main
Mathematics
Inverse Trigonometric Functions
2025 · 4 Apr · Shift 2 · Q40

Inverse Trigonometric Functions question

2025 · 4 Apr · Shift 2 · Q40

JEE MainMathematicsInverse Trigonometric FunctionsMCQ+4 / −1

The sum of the infinite series

\cot ^{-1}\left(\frac{7}{4}\right)+\cot ^{-1}\left(\frac{19}{4}\right)+\cot ^{-1}\left(\frac{39}{4}\right)+\cot ^{-1}\left(\frac{67}{4}\right)+\ldots

. is :

A
$\frac{\pi}{2}+\cot ^{-1}\left(\frac{1}{2}\right)$
B
$\frac{\pi}{2}-\cot ^{-1}\left(\frac{1}{2}\right)$
C
$\frac{\pi}{2}-\tan ^{-1}\left(\frac{1}{2}\right)$
D
$\frac{\pi}{2}+\tan ^{-1}\left(\frac{1}{2}\right)$

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