The value of $\sec ^2\left( an ^{-1} 2 ight)+\operatorname{cosec}^2\left(\cot ^{-1} 3 ight)$ is

Question

The value of $\sec ^2\left(	an ^{-1} 2ight)+\operatorname{cosec}^2\left(\cot ^{-1} 3ight)$ is

Aicharya · Accepted Answer

$\begin{aligned} & 	ext { Let } 	an ^{-1} 2=\alpha \Rightarrow 	an \alpha=2 \ & \quad 	ext { And } \cot ^{-1} 3=\beta \Rightarrow \cot \beta=3 \ & 	herefore \quad \sec ^2\left(	an ^{-1} 2ight)+\operatorname{cosec}^2\left(\cot ^{-1} 3ight) \ & =\sec ^2 \alpha+\operatorname{cosec}^2 \beta \ & =1+	an ^2 \alpha+1+\cot ^2 \beta \ & =2+(2)^2+(3)^2 \ & =15\end{aligned}$

The value of $\sec ^2\left(\tan ^{-1} 2\right)+\operatorname{cosec}^2\left(\cot ^{-1} 3\right)$ is

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