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

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

Vedclass · Accepted Answer

$15$

Vedclass · Answer

(D) We use the trigonometric identities: $\sec ^2 	heta = 1 + 	an ^2 	heta$ and $\operatorname{cosec}^2 	heta = 1 + \cot ^2 	heta$. Let $\alpha = 	an ^{-1} 2$,then $	an \alpha = 2$. Let $\beta = \cot ^{-1} 3$,then $\cot \beta = 3$. The expression becomes: $\sec ^2(	an ^{-1} 2) + \operatorname{cosec}^2(\cot ^{-1} 3) = (1 + 	an ^2(	an ^{-1} 2)) + (1 + \cot ^2(\cot ^{-1} 3))$ $= (1 + 2^2) + (1 + 3^2)$ $= (1 + 4) + (1 + 9)$ $= 5 + 10 = 15$. Thus,the correct option is $D$.

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

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