Evaluate: sec^2(tan^{-1} 2) + csc^2(cot^{-1} | vedclass

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Question

(C) Let $	an^{-1} 2 = \alpha \implies 	an \alpha = 2$.Let $\cot^{-1} 3 = \beta \implies \cot \beta = 3$.The given expression is $\sec^2 \alpha + \cs

Vedclass · Accepted Answer

$15$

Vedclass · Answer

(C) Let $	an^{-1} 2 = \alpha \implies 	an \alpha = 2$.Let $\cot^{-1} 3 = \beta \implies \cot \beta = 3$.The given expression is $\sec^2 \alpha + \csc^2 \beta$.Using the trigonometric identities $\sec^2 	heta = 1 + 	an^2 	heta$ and $\csc^2 	heta = 1 + \cot^2 	heta$,we get:$\sec^2 \alpha + \csc^2 \beta = (1 + 	an^2 \alpha) + (1 + \cot^2 \beta)$.Substituting the values $	an \alpha = 2$ and $\cot \beta = 3$:$= (1 + 2^2) + (1 + 3^2)$$= (1 + 4) + (1 + 9)$$= 5 + 10 = 15$.

Evaluate: $\sec^2(\tan^{-1} 2) + \csc^2(\cot^{-1} 3)$

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