MCQ
મુખ્ય કિંમત શોધો : $\cos ^{-1}\left(-\frac{1}{2}\right)$
- A$\frac{\pi}{2}$
- B$\frac{ \pi}{6}$
- ✓$\frac{2 \pi}{3}$
- D$\frac{5 \pi}{6}$
Then, $\cos y=-\frac{1}{2}=-\cos \left(\frac{\pi}{3}\right)=\cos \left(\pi-\frac{\pi}{3}\right)=\cos \left(\frac{2 \pi}{3}\right)$
We know that the range of the principal value branch of $\cos ^{-1}$ is $[0, \pi]$ and $\cos \left(\frac{2 \pi}{3}\right)=-\frac{1}{2}$
Therefore, the principal value of $\cos ^{-1}\left(-\frac{1}{2}\right)$ is $\left(\frac{2 \pi}{3}\right)$
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