The value of tan ^2≤ft(sec ^-1 2)+cot ^2≤ft(cosec^-1 3) is:

The correct answer is Option (3) → 11

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

$≡\sec^2(\sec^{-1}2)-1+cosec^2(cosec^{-1}3)-1$

$=2^2+3^2-1-1≡4+9-2$

$=11$