Find the value of cos ^{-1}left(cos frac{7 pi | vedclass

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(B) We know that $\cos ^{-1}(\cos x) = x$ if $x \in [0, \pi]$,which is the principal value branch of $\cos ^{-1} x$.Here,$\frac{7 \pi}{6} 
otin [0, \

Vedclass · Accepted Answer

$\frac{5 \pi}{6}$

Vedclass · Answer

(B) We know that $\cos ^{-1}(\cos x) = x$ if $x \in [0, \pi]$,which is the principal value branch of $\cos ^{-1} x$.Here,$\frac{7 \pi}{6} 
otin [0, \pi]$.We use the property $\cos(2\pi - 	heta) = \cos 	heta$ to bring the angle within the principal range.$\cos \left(\frac{7 \pi}{6}ight) = \cos \left(2 \pi - \frac{7 \pi}{6}ight) = \cos \left(\frac{5 \pi}{6}ight)$.Since $\frac{5 \pi}{6} \in [0, \pi]$,we have:$\cos ^{-1}\left(\cos \frac{7 \pi}{6}ight) = \cos ^{-1}\left(\cos \frac{5 \pi}{6}ight) = \frac{5 \pi}{6}$.

Find the value of $\cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)$.

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