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  4. The value of tan2( sec-12)+ cot2(cosec-13) is

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

Inverse Trigonometric Functions

Solution:

$tan^{2} \left(sec^{-1}2 \right) = sec^{2}\left(sec^{-1} 2\right) -1$
$ cot^{2}\left(cosec^{-1} 3\right) = cosec^{2} \left(cosec^{-1} 3\right)-1 $
$ \therefore $ given expression
$ = \left(sec \left(sec^{-1}2\right)\right)^{2} + \left(cosec\left(cosec^{-1}3\right)\right)^{2} - 2 $
$= \left(2\right)^{2} +\left(3\right)^{2}-2 = 11$