# Find the principal values of the following:    2. $\cos^{-1}\left(\frac{\sqrt3}{2} \right )$

D Divya Prakash Singh

So, let us assume that $\cos^{-1}\left(\frac{\sqrt3}{2} \right ) = x$  then,

Taking inverse both sides we get;

$cos\ x = (\frac{\sqrt{3}}{2})$,  or   $cos (\frac{\pi}{6}) = (\frac{\sqrt{3}}{2})$

and as we know that the principal values of $cos^{-1}$ is from [0,$\pi$],

Hence $cos\ x = (\frac{\sqrt{3}}{2})$     when x = $\frac{\pi}{6}$ .

Therefore, the principal value for $\cos^{-1}\left(\frac{\sqrt3}{2} \right )$is   $\frac{\pi}{6}$.

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