^2 ( ^ -1 2 )+cosec^2 ( ^ -1 3 )= - Vidyadip

MCQ

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

A
5
B
13
✓
15
D
6

✓

Answer

Correct option: C.

15

(C) Let $\tan ^{-1} 2=\alpha \Rightarrow \tan \alpha=2$
and $\cot ^{-1} 3=\beta \Rightarrow \cot \beta=3$
$\therefore \quad \sec ^2\left(\tan ^{-1} 2\right)+\operatorname{cosec}^2\left(\cot ^{-1} 3\right)$
$\begin{array}{l}=\sec ^2 \alpha+\operatorname{cosec}^2 \beta=1+\tan ^2 \alpha+1+\cot ^2 \beta \\ =2+(2)^2+(3)^2=15\end{array}$

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