The value of $\tan ^{2}\left(\sec ^{-1} 3\right)+\cot ^{2}\left(\operatorname{cosec}^{-1} 4\right)$ is _________________.
$\tan ^{2}\left(\sec ^{-1} 3\right)+\cot ^{2}\left(\operatorname{cosec}^{-1} 4\right)$
$=\sec ^{2}\left(\sec ^{-1} 3\right)-1+\operatorname{cosec}^{2}\left(\operatorname{cosec}^{-1} 4\right)-1$ $\left(1+\tan ^{2} \theta=\sec ^{2} \theta\right.$ and $\left.1+\cot ^{2} \theta=\operatorname{cosec}^{2} \theta\right)$
$=\left[\sec \left(\sec ^{-1} 3\right)\right]^{2}+\left[\operatorname{cosec}\left(\operatorname{cosec}^{-1} 4\right)\right]^{2}-2$
$=3^{2}+4^{2}-2$
$=9+16-2$
$=23$
Thus, the value of $\tan ^{2}\left(\sec ^{-1} 3\right)+\cot ^{2}\left(\operatorname{cosec}^{-1} 4\right)$ is 23 .
The value of $\tan ^{2}\left(\sec ^{-1} 3\right)+\cot ^{2}\left(\operatorname{cosec}^{-1} 4\right)$ is ___23____.
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