cos left(cos ^{-1}left(-frac{1}{4}right)+sin | vedclass

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Question

(A) We know that for any $x \in [-1, 1]$,the identity $\sin^{-1}(x) + \cos^{-1}(x) = \frac{\pi}{2}$ holds true.Given the expression $\cos \left(\cos ^

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) We know that for any $x \in [-1, 1]$,the identity $\sin^{-1}(x) + \cos^{-1}(x) = \frac{\pi}{2}$ holds true.Given the expression $\cos \left(\cos ^{-1}\left(-\frac{1}{4}\right)+\sin ^{-1}\left(-\frac{1}{4}\right)\right)$.Let $x = -\frac{1}{4}$. Since $x \in [-1, 1]$,we can apply the identity.Therefore,$\cos^{-1}\left(-\frac{1}{4}\right) + \sin^{-1}\left(-\frac{1}{4}\right) = \frac{\pi}{2}$.Substituting this into the original expression,we get $\cos \left(\frac{\pi}{2}\right)$.Since $\cos \left(\frac{\pi}{2}\right) = 0$,the final answer is $0$.

$\cos \left(\cos ^{-1}\left(-\frac{1}{4}\right)+\sin ^{-1}\left(-\frac{1}{4}\right)\right) = $ . . . . . . .

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