The principal solution of ^ -1 ( (7 6 ) ) is

MCQ

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

A
$\frac{7 \pi}{6}$
✓
$\frac{5 \pi}{6}$
C
$\frac{\pi}{6}$
D
$\frac{11 \pi}{6}$

✓

Answer

Correct option: B.

$\frac{5 \pi}{6}$

$\cos ^{-1}\left(\cos \left(\frac{7 \pi}{6}\right)\right)=\cos ^{-1}\left(\cos \left(\pi+\frac{\pi}{6}\right)\right)$
$=\cos ^{-1}\left(-\cos \left(\frac{\pi}{6}\right)\right)$
$=\cos ^{-1}\left(\cos \left(\pi-\frac{\pi}{6}\right)\right)=\cos ^{-1}\left(\cos \left(\frac{5 \pi}{6}\right)\right)=\frac{5 \pi}{6}$

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