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

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(D) Let $	an ^{-1} 2 = \alpha$,which implies $	an \alpha = 2$. Let $\cot ^{-1} 3 = \beta$,which implies $\cot \beta = 3$. We need to evaluate $\sec

Vedclass · Accepted Answer

$15$

Vedclass · Answer

(D) Let $	an ^{-1} 2 = \alpha$,which implies $	an \alpha = 2$. Let $\cot ^{-1} 3 = \beta$,which implies $\cot \beta = 3$. We need to evaluate $\sec ^2 \alpha + \operatorname{cosec}^2 \beta$. Using the trigonometric identities $\sec ^2 	heta = 1 + 	an ^2 	heta$ and $\operatorname{cosec}^2 	heta = 1 + \cot ^2 	heta$: $\sec ^2 \alpha + \operatorname{cosec}^2 \beta = (1 + 	an ^2 \alpha) + (1 + \cot ^2 \beta)$. Substituting the values $	an \alpha = 2$ and $\cot \beta = 3$: $= (1 + 2^2) + (1 + 3^2) = (1 + 4) + (1 + 9) = 5 + 10 = 15$.

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

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