Q72 / 180 · KCET 2025 · Mathematics

$\sec ^2\left(\tan ^{-1} 2\right)+\operatorname{cosec}^2\left(\cot ^{-1} 3\right)=$

  • A
    $1$
  • B
    $5$
  • Correct answer
    C
    $15$
  • D
    $10$

Solution

$\begin{aligned} & =1+\tan ^2\left(\tan ^{-1} 2\right)+1+\cot ^2\left(\cot ^{-1} 3\right) \\ & =1+4+1+9=15\end{aligned}$

Hence, the correct answer is option: 'C'.

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