Find the principal value of each of the following :

Question:

Find the principal value of each of the following :

$\sec ^{-1}(-2)$

Solution:

$\sec ^{-1}(-2)=\pi-\sec ^{-1}(2)\left[\right.$ Formula: $\left.\sec ^{-1}(-x)=\pi-\sec ^{-1}(x)\right]$

$=\pi-\frac{\pi}{3}$

$=\frac{2 \pi}{3}$

 

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