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Mark the tick against the correct answer in the following: The principal value of \cos ^{-1}\left(\frac{-1}{2}\right) is
A. \frac{-\pi}{3}
B. \frac{2 \pi}{3}
C. \frac{4 \pi}{3}
D. \frac{\pi}{3}
CBSE | Class 12 | Inverse Trigonometric Functions | Maths | RS Aggarwal
Mark the tick against the correct answer in the following: The principal value of \cos ^{-1}\left(\frac{-1}{2}\right) is
A. \frac{-\pi}{3}
B. \frac{2 \pi}{3}
C. \frac{4 \pi}{3}
D. \frac{\pi}{3}

Solution:

Option(B) is correct.
To Find: The Principle value of \cos ^{-1}\left(\frac{-1}{2}\right)
Let the principle value be given by x
Now, let x=\cos ^{-1}\left(\frac{-1}{2}\right)
\begin{array}{l} \Rightarrow \cos x=\frac{-1}{2} \\ \Rightarrow \cos x=-\cos \left(\frac{\pi}{3}\right)\left(\because \cos \left(\frac{\pi}{3}\right)=\frac{1}{2}\right) \\ \Rightarrow \cos x=\cos \left(\pi-\frac{\pi}{3}\right)(\because-\cos (\theta)=\cos (\pi-\theta)) \\ \Rightarrow x=\frac{2 \pi}{3} \end{array}

i

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