sin left(cos ^{-1}left(-frac{1}{7}right)+sin | vedclass

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Question

(B) We know the identity $\sin^{-1}(x) + \cos^{-1}(x) = \frac{\pi}{2}$ for $x \in [-1, 1]$.Here,let $x = -\frac{1}{7}$.Since $-\frac{1}{7} \in [-1, 1]

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) We know the identity $\sin^{-1}(x) + \cos^{-1}(x) = \frac{\pi}{2}$ for $x \in [-1, 1]$.Here,let $x = -\frac{1}{7}$.Since $-\frac{1}{7} \in [-1, 1]$,we can apply the identity.Therefore,$\cos^{-1}\left(-\frac{1}{7}\right) + \sin^{-1}\left(-\frac{1}{7}\right) = \frac{\pi}{2}$.Substituting this into the original expression,we get $\sin\left(\frac{\pi}{2}\right)$.Since $\sin\left(\frac{\pi}{2}\right) = 1$,the final answer is $1$.

$\sin \left(\cos ^{-1}\left(-\frac{1}{7}\right)+\sin ^{-1}\left(-\frac{1}{7}\right)\right) = $ . . . . . . .

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