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Inverse Trigonometric Functions question

2022 · 24 Jun · Shift 1 · Q28

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JEE Main
Mathematics
Inverse Trigonometric Functions
2022 · 24 Jun · Shift 1 · Q28

Inverse Trigonometric Functions question

2022 · 24 Jun · Shift 1 · Q28

JEE MainMathematicsInverse Trigonometric FunctionsMCQ+4 / −1

The set of all values of k for which

{({\tan ^{ - 1}}x)^3} + {({\cot ^{ - 1}}x)^3} = k{\pi ^3},\,x \in R

, is the interval :

A
$\left[ {{1 \over {32}},{7 \over 8}} \right)$
B
$\left( {{1 \over {24}},{{13} \over {16}}} \right)$
C
$\left[ {{1 \over {48}},{{13} \over {16}}} \right]$
D
$\left[ {{1 \over {32}},{9 \over 8}} \right)$

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