Question:
Find the principal value of each of the following :
$\sec ^{-1}\left(\frac{-2}{\sqrt{3}}\right)$
Solution:
$\sec ^{-1}\left(\frac{-2}{\sqrt{3}}\right)=\pi-\sec ^{-1}\left(\frac{2}{\sqrt{3}}\right)\left[\right.$ Formula: $\left.\sec ^{-1}(-x)=\pi-\sec ^{-1}(x)\right]$
$=\pi-\frac{\pi}{6}$
$=\frac{5 \pi}{6}$
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