MCQ
મુખ્ય કિંમત શોધો : $\cos ^{-1}\left(-\frac{1}{\sqrt{2}}\right)$
- A$\frac{2 \pi}{3}$
- B$\frac{5 \pi}{6}$
- ✓$\frac{3 \pi}{4}$
- D$\frac{3 \pi}{2}$
Then $\cos y=-\frac{1}{\sqrt{2}}=-\cos \left(\frac{\pi}{4}\right)=\cos \left(\pi-\frac{\pi}{4}\right)=\cos \left(\frac{3 \pi}{4}\right)$
We know that the range of the principal value branch of $\cos ^{-1}$ is $[0, \pi]$ and $\cos \left(\frac{3 \pi}{4}\right)=-\frac{1}{\sqrt{2}}$
Therefore, the principal value of $\cos ^{-1}\left(-\frac{1}{\sqrt{2}}\right)$ is $\frac{3 \pi}{4}$
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