sec ^2(tan ^{-1} 2)+operatorname{cosec}^2(cot | vedclass

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(C) We use the trigonometric identities $\sec ^2 	heta = 1 + 	an ^2 	heta$ and $\operatorname{cosec}^2 	heta = 1 + \cot ^2 	heta$. Substituting $

Vedclass · Accepted Answer

$15$

Vedclass · Answer

(C) We use the trigonometric identities $\sec ^2 	heta = 1 + 	an ^2 	heta$ and $\operatorname{cosec}^2 	heta = 1 + \cot ^2 	heta$. Substituting $	heta = 	an ^{-1} 2$ and $	heta = \cot ^{-1} 3$ respectively: $= (1 + 	an ^2(	an ^{-1} 2)) + (1 + \cot ^2(\cot ^{-1} 3))$ $= (1 + (	an(	an ^{-1} 2))^2) + (1 + (\cot(\cot ^{-1} 3))^2)$ $= (1 + 2^2) + (1 + 3^2)$ $= (1 + 4) + (1 + 9)$ $= 5 + 10 = 15$.

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

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