cos left[ {{cos }^{ - 1}}left( {frac{{ - 1}}{ | vedclass

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(B) We know the identity for inverse trigonometric functions: $\sin^{-1}(x) + \cos^{-1}(x) = \frac{\pi}{2}$ for $x \in [-1, 1]$.In the given expressio

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$0$

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(B) We know the identity for inverse trigonometric functions: $\sin^{-1}(x) + \cos^{-1}(x) = \frac{\pi}{2}$ for $x \in [-1, 1]$.In the given expression,let $x = -\frac{1}{7}$.Since $-\frac{1}{7} \in [-1, 1]$,we can apply the identity:$\cos^{-1}\left( -\frac{1}{7} \right) + \sin^{-1}\left( -\frac{1}{7} \right) = \frac{\pi}{2}$.Substituting this into the original expression:$\cos \left[ \cos^{-1}\left( -\frac{1}{7} \right) + \sin^{-1}\left( -\frac{1}{7} \right) \right] = \cos \left( \frac{\pi}{2} \right)$.Since $\cos \left( \frac{\pi}{2} \right) = 0$,the final result is $0$.

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

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