Find the value of cos ^{-1}left(frac{1}{2}rig | vedclass

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(B) Let $\cos ^{-1}\left(\frac{1}{2}\right)=x$. Then,$\cos x=\frac{1}{2}=\cos \left(\frac{\pi}{3}\right)$. Therefore,$\cos ^{-1}\left(\frac{1}{2}\righ

Vedclass · Accepted Answer

$\frac{2 \pi}{3}$

Vedclass · Answer

(B) Let $\cos ^{-1}\left(\frac{1}{2}ight)=x$. Then,$\cos x=\frac{1}{2}=\cos \left(\frac{\pi}{3}ight)$. Therefore,$\cos ^{-1}\left(\frac{1}{2}ight)=\frac{\pi}{3}$. Let $\sin ^{-1}\left(\frac{1}{2}ight)=y$. Then,$\sin y=\frac{1}{2}=\sin \left(\frac{\pi}{6}ight)$. Therefore,$\sin ^{-1}\left(\frac{1}{2}ight)=\frac{\pi}{6}$. Substituting these values into the expression: $\cos ^{-1}\left(\frac{1}{2}ight)+2 \sin ^{-1}\left(\frac{1}{2}ight)=\frac{\pi}{3}+2 	imes \frac{\pi}{6} = \frac{\pi}{3}+\frac{\pi}{3} = \frac{2 \pi}{3}$.

Find the value of $\cos ^{-1}\left(\frac{1}{2}\right)+2 \sin ^{-1}\left(\frac{1}{2}\right)$

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