MCQ
The principal solution of $\cos ^{-1}\left(\cos \left(\frac{7 \pi}{6}\right)\right)$ is
- A$\frac{7 \pi}{6}$
- B$\frac{5 \pi}{6}$
- C$\frac{\pi}{6}$
- D$\frac{11 \pi}{6}$
✓
Answer
$
\begin{array}{l}
\text {(b) : } \cos ^{-1}\left(\cos \left(\frac{7 \pi}{6}\right)\right)=\cos ^{-1}\left(\cos \left(\pi+\frac{\pi}{6}\right)\right) \\
=\cos ^{-1}\left(-\cos \left(\frac{\pi}{6}\right)\right) \\
=\cos ^{-1}\left(\cos \left(\pi-\frac{\pi}{6}\right)\right)=\cos ^{-1}\left(\cos \left(\frac{5 \pi}{6}\right)\right)=\frac{5 \pi}{6}
\end{array}
$
\begin{array}{l}
\text {(b) : } \cos ^{-1}\left(\cos \left(\frac{7 \pi}{6}\right)\right)=\cos ^{-1}\left(\cos \left(\pi+\frac{\pi}{6}\right)\right) \\
=\cos ^{-1}\left(-\cos \left(\frac{\pi}{6}\right)\right) \\
=\cos ^{-1}\left(\cos \left(\pi-\frac{\pi}{6}\right)\right)=\cos ^{-1}\left(\cos \left(\frac{5 \pi}{6}\right)\right)=\frac{5 \pi}{6}
\end{array}
$
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