cot ^{-1}left(2 cos left(2 operatorname{cosec | vedclass

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Question

(A) We are given the expression $\cot ^{-1}\left(2 \cos \left(2 \operatorname{cosec}^{-1}(\sqrt{2})\right)\right)$.First,evaluate $\operatorname{cosec

Vedclass · Accepted Answer

$\frac{\pi}{2}$

Vedclass · Answer

(A) We are given the expression $\cot ^{-1}\left(2 \cos \left(2 \operatorname{cosec}^{-1}(\sqrt{2})ight)ight)$.First,evaluate $\operatorname{cosec}^{-1}(\sqrt{2})$.Since $\operatorname{cosec}(\frac{\pi}{4}) = \sqrt{2}$,we have $\operatorname{cosec}^{-1}(\sqrt{2}) = \frac{\pi}{4}$.Now,substitute this into the expression:$2 \cos \left(2 	imes \frac{\pi}{4}ight) = 2 \cos \left(\frac{\pi}{2}ight)$.Since $\cos \left(\frac{\pi}{2}ight) = 0$,the expression becomes $2 	imes 0 = 0$.Finally,we need to find $\cot ^{-1}(0)$.Since $\cot \left(\frac{\pi}{2}ight) = 0$,we have $\cot ^{-1}(0) = \frac{\pi}{2}$.Thus,the correct option is $A$.

$\cot ^{-1}\left(2 \cos \left(2 \operatorname{cosec}^{-1}(\sqrt{2})\right)\right)=\ldots$

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