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Q. $\sec^2(\tan^{-1}2)+cosec^2(\cot^{-1}3)=$

Inverse Trigonometric Functions

Solution:

$sec^{2}\left(tan^{-1}2\right) = 1 +tan^{2}\left(tan^{-1}2\right)$
$= 1+\left(2\right)^{2} = 5 $
$ cosec^{2}\left(cot^{-1} 3\right) = 1+ cot^{2} \left(cot^{-1} 3\right)$
$= 1+\left(3\right)^{2} = 10$
$ \therefore $ reqd. value $= 5+10 $
$ = 15$