Evaluate: sec^{-1} x + operatorname{cosec}^{- | vedclass

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Question

(A) We know the standard identity for inverse trigonometric functions: $\sec^{-1} x + \operatorname{cosec}^{-1} x = \frac{\pi}{2}$ for $|x| \geq 1$. S

Vedclass · Accepted Answer

$\pi$

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(A) We know the standard identity for inverse trigonometric functions: $\sec^{-1} x + \operatorname{cosec}^{-1} x = \frac{\pi}{2}$ for $|x| \geq 1$. Similarly,for $|x| \geq 1$,we have $\cos^{-1}(x^{-1}) + \sin^{-1}(x^{-1}) = \frac{\pi}{2}$. Substituting these identities into the given expression: $\sec^{-1} x + \operatorname{cosec}^{-1} x + \cos^{-1}(x^{-1}) + \sin^{-1}(x^{-1}) = \frac{\pi}{2} + \frac{\pi}{2} = \pi$. Thus,the correct option is $A$.

Evaluate: $\sec^{-1} x + \operatorname{cosec}^{-1} x + \cos^{-1}(x^{-1}) + \sin^{-1}(x^{-1})$ (where $|x| > 1, x \in R$)

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