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Mark the tick against the correct answer in the following:

Question:

Mark the tick against the correct answer in the following:

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

A. $\frac{\pi}{6}$

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

C. $\frac{7 \pi}{6}$

D. none of these

 

Solution:

To Find:The Principle value of $\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$

Let the principle value be given by $\mathrm{x}$

Now, let $x=\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$

$\Rightarrow \cos x=\frac{\sqrt{3}}{2}$

$\Rightarrow \cos x=\cos \left(\frac{\pi}{6}\right)\left(\because \cos \left(\frac{\pi}{6}\right)=\frac{\sqrt{3}}{2}\right)$

$\Rightarrow \mathrm{x}=\frac{\pi}{6}$

 

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