Find the principal value of ^ -1 ( 3 2 ) - Vidyadip

Question

Find the principal value of $\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$

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Answer

Let $\cos^{-1}\left(\frac{\sqrt{3}}{2}\right) = x$
Then, $\cos x = \frac{\sqrt{3}}{2} = \cos \left(\frac{\pi}{6}\right)$
We know that the principle value range of $\cos^{-1}$ is $[0, \pi]$
and $\cos \left(\frac{\pi}{6}\right)=\frac{\sqrt{3}}{2}$
Therefore, the principal value of $cos^{-1}$ $\left(\frac{\sqrt{3}}{2}\right) \text { is } \frac{\pi}{6}$

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