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 :

Question

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 :

$\left[ {{1 \over {32}},{7 \over 8}} \right)$

$\left( {{1 \over {24}},{{13} \over {16}}} \right)$

$\left[ {{1 \over {48}},{{13} \over {16}}} \right]$

$\left[ {{1 \over {32}},{9 \over 8}} \right)$

Please login to view the detailed solution steps...