The value of $\cos ^{-1}\left(\cos \left(\frac{7 \pi}{6}\right)\right)$ is

The value of $\cos ^{-1}\left(\cos \left(\frac{7 \pi}{6}\right)\right)$ is
  1. $\frac{5 \pi}{6}$
  2. $\frac{\pi}{3}$
  3. $\frac{7 \pi}{6}$
  4. $\frac{\pi}{6}$

Solution

The value of \(\cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)\)
\(\begin{aligned}
& =\cos ^{-1}\left[\cos \left(2 \pi-\frac{5 \pi}{6}\right)\right] \\
& =\cos ^{-1}\left(\cos \frac{5 \pi}{6}\right) \\
& =\frac{5 \pi}{6}
\end{aligned}\)

Asked in: MHT CET 2020 (19 Oct Shift 1)

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