The value of tan ^2(sec ^{-1} 4) + cot ^2(ope | vedclass

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(C) Let $	heta_1 = \sec ^{-1} 4$,then $\sec 	heta_1 = 4$. Using the identity $	an ^2 	heta = \sec ^2 	heta - 1$,we get $	an ^2(\sec ^{-1} 4) = \

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$23$

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(C) Let $	heta_1 = \sec ^{-1} 4$,then $\sec 	heta_1 = 4$. Using the identity $	an ^2 	heta = \sec ^2 	heta - 1$,we get $	an ^2(\sec ^{-1} 4) = \sec ^2(\sec ^{-1} 4) - 1 = 4^2 - 1 = 16 - 1 = 15$. Let $	heta_2 = \operatorname{cosec}^{-1} 3$,then $\operatorname{cosec} 	heta_2 = 3$. Using the identity $\cot ^2 	heta = \operatorname{cosec}^2 	heta - 1$,we get $\cot ^2(\operatorname{cosec}^{-1} 3) = \operatorname{cosec}^2(\operatorname{cosec}^{-1} 3) - 1 = 3^2 - 1 = 9 - 1 = 8$. Adding these values,we get $15 + 8 = 23$.

The value of $\tan ^2(\sec ^{-1} 4) + \cot ^2(\operatorname{cosec}^{-1} 3)$ is

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